The Faroese has suffered a thigh knock and is now doubtful to be available to face Ross County tomorrow.
Lee Hollis, the Fir Park club's other senior goalkeeper, is also still to recover from injury so the club have turned to Twardzik - a 22-year-old Czech who has still to make his debut at Dens Park.
"It has been a whirlwind 24 hours," said Twardzik. "I was here in 2009 in pre-season. I tried to get away from Bayern Munich but they tried to get compensation and I had to leave. I'm happy to be back, even if it's only for a couple of weeks."
Manager Stuart McCall added: "We are grateful to Dundee for letting him come. I spoke to John Brown, who speaks highly of him."