Andrews was hospitalized while undergoing tests to pinpoint the cause of the clots, sources said. He was released from the hospital Monday night.
A team captain in his fifth NFL season, Andrews played 28 snaps in the Patriots' preseason win over the Carolina Panthers on Thursday but wasn't at practice the past two days.
Andrews' leadership and steadiness have been critical for the Patriots since he became a full-time starter in 2016, as he developed a rapport with quarterback Tom Brady. With Andrews at center and up-and-coming Joe Thuney (fourth year) and Shaq Mason (fifth year) as starting guards, the interior of the line has been one of the strengths of the team.
Andrews, 27, has played in 60 career regular-season games (57 starts), in addition to making nine playoff starts. The University of Georgia alumnus, who made the team as an undrafted free agent in 2015, was the starter in each of the Patriots' past three Super Bowl appearances.
The Athletic first reported Andrews' condition.
Earlier Monday, Patriots offensive line coach Dante Scarnecchia -- while taking a wait-and-see approach on Andrews' condition -- said that he believes the attrition the team has already experienced on the line with multiple retirements hasn't left the unit short-handed.
"We got what we got. The cavalry, they're not coming over the hill," he said. "But we have good players. I like the guys we got."
Andrews was not fully healthy early in training camp. He missed the team's first few practices before returning on a limited basis.
Patriots coach Bill Belichick previously noted that centers are in the middle of every play, so communication -- coupled with angles and gaining favorable position -- is a big part of the job description.
"David's good at all those things," Belichick said in 2017. "He has a lot of experience in his life playing center. I think a lot of those things come pretty naturally to him, the understanding of how far you have to go, how quickly you have to get there, how close in proximity is your teammate, where is the play designed to run and so forth. He has a good instinct for the position."