Defender Sviatchenko damaged knee ligaments during Wednesday's 1-0 win away to Rosenborg and will not feature against play-off opponents Astana.
The Denmark player was on crutches after getting injured in Norway.
"It could have been worse but we will take it at six weeks, not probably back until September," said Rodgers.
"We've just had his results so he will probably be up to about six weeks, which is disappointing."
Midfielder Nir Bitton came on for former Midtjylland player Sviatchenko in Trondheim as Celtic beat Rosenborg by a single goal on the night and on aggregate to progress to the play-off round.
Rodgers is also without Belgian defender Dedryck Boyata until September.
Erik Sviatchenko will miss Celtic's Champions League play-off matches as boss Brendan Rodgers confirmed the Dane will miss "up to about six weeks".