Harlequins prop Leonard made his 100th Test match appearance in England's 25-17 victory over France at Twickenham.
But he was forced out of the action seven minutes before half-time and his prospects of facing Wales in Cardiff don't look good.
Leonard has admitted that he has no idea at this stage whether he will be fit for the Wales game.
"I tried to run the injury off, but it just didn't happen," he said. "I haven't got a clue about next Saturday. We will look at it in greater detail next week."
England boss Clive Woodward was equally pessimistic, adding: "Jason has pulled a hamstring, and he is pretty down. It is not great for next week."
If Leonard is ruled out, then Leicester prop Graham Rowntree would be his likely replacement as England look for a second championship victory.
Despite losing their hugely-experienced front-row forward and losing the try-count 3-1, England still prevailed in front of a 73,500 crowd.
"I am very pleased that we won. It has been a difficult week and it is hats off to the players," Woodward added.
"We will be self-critical about this performance. We built a 25-7 lead but then we probably produced the worst 25 minutes we have played for a long, long time.
"In the end, we were stronger than them, and it is certainly a lot nicer being in this position than the one we were in 12 months ago when we lost in Paris.
"We didn't keep hold of the ball from numbers one to 15, and for some reason we decided to kick the ball away. We lost some direction and composure during those last 25 minutes.
"When (Jason) Robinson scored, I thought that the French were hanging on and I thought that there were 40 or 50 points on the board for us.
"We are keeping our feet firmly on the ground. We didn't have the pace and intensity that we had during the autumn internationals, but I don't think that France did either."