Wade Phillips said Colombo is expected to have surgery on Monday.
Colombo was injured on the first play of a second-quarter drive when Packers defensive tackle Johnny Jolly rolled up on the back of his leg. He was immediately taken off the field for X-rays before the team announced he had a broken left fibula.
Phillips later confirmed that Colombo had a high ankle sprain and broken fibula.
"He's not necessarily out for the season. That remains to be seen," Phillips said.
Colombo, a former first-round pick by the Bears in 2002, has started every game for Dallas since 2006 - a string of 57 in a row.
"He's been a staple over there for a while now, and that's going to be very tough," Tony Romo said. "He's been playing there for a long time, he's been playing at a high level."
The Cowboys had been one of just eight teams in the NFL to start the same lineup on the offensive line every game this year. That will obviously change next week with the loss of Colombo.