Head coach Tom Coughlin said Andrews is expected to make a full recovery and be able to resume his playing career.
"Very serious medical condition," Coughlin said. "He just can't go back to football right now."
The team's backup offensive lineman, often used as an extra blocking lineman for the Giants, was admitted to Hackensack University Medical Center Saturday night and is expected to be released on Monday. The Giants say Andrews' blood clots are believed to have originated in his legs, before breaking up and traveling to his lungs.
Coughlin did not have an update on safety Kenny Phillips, who was at the Hospital for Special Surgery having his sprained left knee examined. Phillips was initially diagnosed by team doctors with an medial collateral ligament sprain, a team source told ESPN's NFL Insider Adam Schefter.
Phillips said after the Giants' 38-35 loss to Green Bay that he was going for an MRI on Monday morning. He did say that his left anterior cruciate ligament is "good." Phillips underwent surgery on his left knee two seasons ago.
Coughlin said he wasn't positive about the severity of Phillips' injury. The safety could miss a few weeks if it's a MCL sprain.
"We will find out," Coughlin said. "I am not sure yet. I've seen guys jump off and run off the field and next day it's an ACL (tear)."
Coughlin also said that center David Baas is being examined for the headaches that kept him out of Sunday's loss.
"He is going to spend a great deal of today with various medical people to see what it is," Coughlin said. "I am not sure about it. We do have an idea and we are going into that direction but I wouldn't want to say anything until it is proven but hopefully it can be gotten under control."
Osi Umenyiora is considered day to day with an ankle injury that kept him out of Sunday's game. However, the defensive end is expected to miss this Sunday night's game against Dallas.
Defensive end Dave Tollefson has a bruised right knee. Coughlin also said that running back Ahmad Bradshaw (foot) and linebacker Michael Boley (hamstring) came out of Sunday's game feeling sore but did not suffer any setbacks.
Ohm Youngmisuk covers the Giants for ESPNNewYork.com.