The Poland international had to come off immediately after Gary Cahill equalised in the Premier League clash at Stamford Bridge 10 minutes into the second half.
Paulo Gazzaniga came on to replace the former Celtic man and the young Argentine keeper was beaten by John Terry and Demba Ba as Chelsea went on to secure all three points.
Southampton boss Mauricio Pochettino revealed Boruc would have scans on his hand and wrist on Sunday evening.
He said: "We do not know (how bad the injury is) at the moment.
"He is going to hospital to have X-rays done so that we can know exactly what has happened to his hand or wrist."
Pochettino was left to rue his side’s inability to hold on to their early lead, but believes they can learn from a second consecutive defeat that leaves them seventh in the table.
He said: "We had a great start. That was amazing. Before we conceded those goals, we were doing well.
"I think we were doing quite well going into the second half. We corrected a lot of things after half-time.
"This is a learning process. We're always learning. We're the youngest team in the league. We have to keep on learning.
"It's clear that the game changed when we scored the goal so early on. After that, I think we competed well.
"They were soft goals that we shouldn't have conceded - that definitely influenced the game in the end."
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