Right-back Reid, who sustained a similar setback earlier in the campaign, will undergo a scan to assess the full extent of the damage.
Hodgson said: "Funnily enough, the last time Steven missed a few weeks was when he turned over his ankle at Newcastle and he has done the same this time.
"We don't believe it is going to be a major injury and we will see what the scan shows.
"But experience of these things shows that all these ligament injuries take a few weeks.
"Luckily Tamas came on against Chelsea and did well while Billy Jones should not be out for too much longer with his hamstring injury.
"We are fortunate overall at the moment in not having too many injuries.''
Skipper Chris Brunt marked his comeback from two months out of action with a broken foot by playing the final half-hour against Chelsea.
Hodgson said: "It was good for Chris to get in 30 minutes. He hadn't played any competitive football and any longer than 30 minutes would have been quite tough.''