The Newcastle forward hobbled off after 34 minutes, having tweaked the muscle as he unleashed a shot that was tipped over the bar by goalkeeper Alex Manninger.
Owen has struggled with a series of injuries since damaging anterior cruciate ligaments in his knee during last summer's World Cup and he is now expected to be out for a further month.
England is in danger of failing to qualify for Euro 2008. The team needs Croatia to lose away to Macedonia FYR Saturday, or Russia to lose in Israel. England would then have to beat Croatia to qualify for the championship, hosted by Austria and Switzerland.
They will already be without the injured Wayne Rooney and Emile Heskey for that game, and the loss of Owen, England's fourth top scorer of all time, is a major set-back.
"It's a huge blow," admitted midfielder Frank Lampard. "If results go our way Wednesday is an opportunity to qualify.
"Michael always produces in big games. Crouchy (Peter Crouch) has shown what he can do. Jermain Defoe came on and he'll be sharp," Lampard added.
Manager Steve McClaren was just as frustrated, but tried to be positive.
"Injuries are part of football," he said. "If we have to win on Wednesday we go in without our two centre-backs and two centre-forwards.
"But we have enough spirit in the dressing-room. Now we just have to sit and wait. We're in a vacuum."
It could have been worse for England as well, with Peter Crouch involved in an ugly collision with Austrian goalkeeper Jurgen Macho.
Macho swallowed his tongue and suffered a damaged shoulder, but Crouch somehow escaped unscathed. Manninger came on as a replacement for Macho.
The Liverpool forward, without a Premiership goal since March, also got the only goal of the game a minute before half-time.
David Beckham's corners were a menace all night and, on this occasion, Crouch met his looping delivery with a powerful downward header that skipped up off the turf and into the top corner.
That improves his already impressive goalscoring record to 11 goals in the 13 matches he has started for England.
"It's difficult to come away from home," Crouch said. "The main objective is Wednesday. We've got to hope for the right results Saturday, but today was about a run out and we got another win to take in to Wednesday."
For now all England's players can do is wait for the results in Skopje and Tel Aviv.
"We'll all be waiting and hoping," Lampard said.