Marlo Spaeth started working as a sales associate at a Walmart in Manitowoc, Wis., in 1999, folding towels, cleaning aisles, processing returns and greeting customers, her lawyers said. Over the next 15 years, she received several pay raises and positive performance reviews.

One manager wrote that she was “great with customers” and a “very hard worker.” Another manager wrote, “Marlo is a very friendly person and is a delight to have working here.”

But Ms. Spaeth’s hours suddenly shifted in November 2014, when Walmart instituted a computerized scheduling system, which the company said was based on customer traffic and was designed to ensure that enough people were working when the store was busiest.

Ms. Spaeth was expected to work from 1 p.m. to 5:30 p.m., rather than her previous schedule of noon to 4 p.m., her lawyers said.

The abrupt change represented a significant hardship for Ms. Spaeth, who has Down syndrome and thrives on routine, her lawyers said. Ms. Spaeth repeatedly told a manager that she wanted her old schedule back, her lawyers said.

“She’s afraid she’s going to miss the bus,” her sister and guardian, Amy Jo Stevenson, said she had told a Walmart manager, according to court records. “She’s afraid she’s going to miss dinner. It’s upsetting to her. She gets too hot. She says she feels sick, and she can’t accommodate it, so we need it switched back for her.”

But the company refused to switch Ms. Spaeth back to her old schedule at the store, which was open 24 hours a day and had more than 300 employees, her lawyers said. Walmart then took disciplinary action against Ms. Spaeth twice for absenteeism and tardiness, her lawyers said.

On July 10, 2015, Walmart fired Ms. Spaeth for excessive absenteeism.

A Walmart training coordinator took Ms. Spaeth’s vest and walked her out of the store where she had worked for about 16 years. The training coordinator later testified that both she and Ms. Spaeth had been crying and that Ms. Spaeth had not understood what was happening, court records show.

Ms. Spaeth and her mother and sister met with Walmart managers and asked that she be rehired and allowed to return to her old schedule, her lawyers said. But Walmart refused to rehire her, even though her termination letter said she could be hired again, her lawyers said.

On Thursday, a jury in U.S. District Court for the Eastern District of Wisconsin, in Green Bay, found that Walmart had violated the Americans With Disabilities Act, which bans discrimination based on an employee’s disability, and awarded Ms. Spaeth $125 million in punitive damages and $150,000 in compensatory damages.

The jury, which deliberated for three hours after a four-day trial, found that Walmart had failed to provide Ms. Spaeth with a reasonable accommodation, even though she needed one because she has Down syndrome and it would not have posed a hardship to the company.

The jury also found that Walmart had fired Ms. Spaeth and then failed to rehire her because she has a disability.

“The jury here recognized, and apparently was quite offended, that Ms. Spaeth lost her job because of needless — and unlawful — inflexibility on the part of Walmart,” said Gregory Gochanour, a lawyer with the Equal Employment Opportunity Commission, which had sued Walmart on behalf of Ms. Spaeth.

Walmart said in a statement that the verdict would be reduced to $300,000, which is the maximum amount allowed under federal law for compensatory and punitive damages.

“We do not tolerate discrimination of any kind, and we routinely accommodate thousands of associates every year,” Walmart said. “We often adjust associate schedules to meet our customers’ expectations and while Ms. Spaeth’s schedule was adjusted, it remained within the times she indicated she was available.”

The company said that it was “sensitive to this situation and believe we could have resolved this issue with Ms. Spaeth.” It added, “However, the E.E.O.C.’s demands were unreasonable.”

An E.E.O.C. lawyer declined to comment, but the agency’s website notes that compensatory and punitive damages are capped at $300,000 for employers with more 500 workers.

Walmart, which employs more than 2.3 million people around the world, is the nation’s largest private employer, with more than 1.6 million employees in the United States, according to its website.

Julianne Bowman, the Chicago district director at the E.E.O.C., said employers, no matter how large, had an obligation under the law to evaluate the individual circumstances of employees with disabilities when considering requests for reasonable accommodations.

“Ms. Spaeth’s request was a simple one and denying it profoundly altered her life,” Ms. Bowman said in a statement.

Dr. David Smith, a former program director at the Down Syndrome Clinic of Wisconsin in Milwaukee, said in court papers that people with Down syndrome need routines to manage their day and may not have the cognitive ability to adjust well to changes.

When Walmart changed Ms. Spaeth’s schedule, the stress of the change and the pressure she felt to adapt to her new hours may have thrown her off, he said.

People with Down syndrome “make very good employees if they have the right job and an understanding employer,” said Dr. Smith, who was an expert witness for the E.E.O.C.

“Their job becomes a major focus of their life, and gives them a sense of self-worth,” he said. “When Ms. Spaeth’s schedule was changed, she was unable to adapt to that variation.”