Luigi Mangione was arrested in Altoona, Pennsylvania, after he was spotted at a McDonald's by someone who believed he resembled the gunman, officials said at a news conference.
Thompson, 50, was gunned down outside a Manhattan hotel early on Wednesday morning by a masked man who appeared to wait for his arrival before shooting the executive from behind.
Police have not publicly identified a motive but have said Thompson appeared to be deliberately targeted.
The words "deny," "defend" and "depose" were carved into shell casings found at the scene, several news outlets have reported. The words evoke the title of a book critical of the insurance industry published in 2010 titled "Delay, Deny, Defend: Why Insurance Companies Don't Pay Claims and What You Can Do About It."
The suspect ran from the scene and then rode a bike into Central Park. Surveillance video captured him exiting the park and taking a taxi to a bus station in northern Manhattan, where police believe he used a bus to flee the city.
Thompson, a father of two, had been CEO of UnitedHealth Group's insurance unit since April 2021, part of a 20-year career with the company. He had been in New York to attend the company's annual investor conference.
A UnitedHealth spokesperson declined to comment on the latest reports.