The high-profile recruit was forced off the field in the Sky Blues' 3-0 win over rivals Melbourne Victory after setting up Joe Lolley's second goal in the 26th minute.
Sydney coach Ufuk Talay confirmed the extent of Costa's injury on Thursday, ahead of their round 12 clash in Newcastle.
Talay has earmarked their AFC Champions League 2 (ACL2) match on February 12 against Thai Premier League club Bangkok United as a return for Costa.
At worst, the 34-year-old winger could be out for eight weeks.
"Not good," Talay said of the Brazilian's injury.
"We'll just make sure we get him right and push him again.
"If we can push him to that first leg of the ACL, that means he's come back a little bit early.
"He's probably as frustrated as I am."
Look away now — Paramount+ Australia (@ParamountPlusAU) @SydneyFC fans 😬Douglas Costa looks to have twanged his hammy and has made his exit for this edition of the #BigBlueWe're back underway in #SYDvMVC LIVE on Paramount+ pic.twitter.com/QeUMFfEknMDecember 28, 2024
Costa had missed three weeks earlier in the season with the same injury, picking up the issue in their ACL2 match against Japanese side Sanfrecce Hiroshima in October after making his A-League Men debut in round one.
He returned to feature in their round five triumph over Western Sydney before finally hitting the scoresheet four weeks later in the 3-3 draw against Adelaide United.
The Reds had got off to a perfect start thanks to Archie Goodwin and Stefan Mauk goals, before Costa scored twice and added an assist to salvage a point.
His assist against the Victory was his fourth goal involvement in two games, and he played a part in Sydney securing their first clean sheet of the season.
They are ninth on 13 points, while the Jets are 11th on six.
"He was enjoying himself. He had a really good first half against Melbourne Victory," Talay said.
"I thought we got him into a really good place physically but these things happen in football."
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