The Town skipper has made the temporary switch to the Sky Bet Championship strugglers after finding himself out of the first-team picture at Portman Road.
Edwards, 35, has not played for Ipswich since the 2-0 home win over Reading on January 25 and will be out of contract at the end of the season.
He told the club's official website: "It's important for me at this stage of my career to be playing football week in, week out.
"When I heard Millwall were keen to take me, I jumped at the chance to go there and play games.
"I wish Ipswich well and I hope when I come back to the club at the end of the season that I will be available for the play-offs."
Town manager Mick McCarthy added: "He wants to play games but he's not done that here lately.
"We have other lads in front of him, so it's an opportunity for Carlos to go out and play some first-team football and we wish him well."
Trinidad and Tobago international Edwards could make his debut for Ian Holloway's Millwall side in Saturday's home game against Blackburn Rovers.