Suk-Young suffered the injury in training last week and subsequently missed the goalless stalemate against South Yorkshire rivals Barnsley at Oakwell on Saturday, where news broke that long-serving chairman John Ryan had resigned his post after a fall-out with the Rovers board.
South Korean Suk-Young was signed from QPR towards the end of October on a deal until December 31 following the injury to left-back James Husband and his absence adds to manager Paul Dickov's defensive problems.
"It feels like there's a little bit of a curse going on at the moment," said the Doncaster boss.
"He just went for a ball in training on Friday with nobody around him and he's rolled his ankle. He's going to be out for six weeks.
"If you add that to James Husband and Rob Jones, and big Jamie McCombe's out as well, we're right back where we started."