The 33-year-old suffered the injury in February playing for Western Australia.
He aggravated it on the eve of a planned comeback in March and is likely to miss the start of the new season.
"It could be a couple of weeks, it could be longer," said Glamorgan's Toby Radford, coach of the County Championship Division Two side.
"As soon as we can get the proper scan done we'll know where we stand."
Glamorgan begin their Division Two campaign at Leicestershire on 12 April before facing Surrey at home a week later.
Hogan has been a crucial strike bowler for Glamorgan in the last two seasons, claiming 98 wickets in all competitions last season despite missing three weeks on paternity leave.
"He was running around [at Swalec Stadium] and looking in good shape in some ways, [but] we just don't know how bad the injury is," Radford told BBC Wales Sport.
"He only gets pain when he bowls so we'll have a scan next week, see where he's at and then we can make a real plan for when he returns."
Radford is keeping open the option of signing a loan player or going into the Leicestershire game with his current bowling resources, despite the inexperience of several players.
"It is [inexperienced], but Ruaidhri Smith didn't do himself any harm [against Cardiff MCCU], David Lloyd batted and bowled well, and Craig Meschede bowled very well."
Will Owen and Dewi Penrhyn-Jones are the other seam bowlers available to Radford.
Jack Murphy is also on the county's staff, but took two wickets playing against them for the Cardiff universities team, in Glamorgan's final warm-up match.
The match ended in a draw with Glamorgan scoring 434-7 and Cardiff MCCU 110-8.
Glamorgan fast bowler Michael Hogan faces a second scan on a hamstring injury to determine how long he is likely to be sidelined.