Bertrand, 28, is yet to miss a league match for Southampton this campaign but limped off in the final stages of the game at Stamford Bridge with the Saints yet to release details of either players' injuries or recovery timelines.
"Unfortunately, in the game against Chelsea, I suffered an injury that will keep me away from the next few games. Thank you all for the messages and support," Soares said on his official Instagram account.
The injuries leave Southampton manager Mauricio Pellegrino with limited options at the back as the club aim to end a poor run of three defeats and two draws in their last five league games.
Southampton are 12th in the league and host 11th-placed Huddersfield Town on Saturday.
(Reporting by Aditi Prakash in Bengaluru; Editing by Christian Radnedge)
