The Blues claimed a 21-9 win at BT Sport Cardiff Arms Park on Friday night but it was soured slightly with the news that Warburton had picked up a knock.
The 26-year-old has appeared in six GUINNESS PRO12 games for the Welsh outfit this season, scoring a try against Leinster in September.
The injury is similar to the one he suffered in Wales' win over South Africa last month, and rules him out of the visit of Newport Gwent Dragons on Friday.
But Hammett, who admitted he would have rested the Wales captain regardless of injury, expects him to be back in contention for the Round 12 reverse fixture against the Dragons.
"He had a bit of a stinger… I think it will only be one week," Hammett told BBC Sport.
"He's had two games and, as it is, I would have managed him for one of these games anyway."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the GUINNESS PRO12
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland