The striker, a summer buy from Bristol Rovers, missed Saturday's friendly against Tottenham at the Amex Stadium due to the problem.
Ashley Barnes deputised for Hoskins and scored Albion's first senior goal at their new home to give manager Gus Poyet a potential selection dilemma ahead of next weekend's Championship opener against Doncaster.
And Poyet says there is still time for his squad members to stake a claim to be in the line-up for the first competitive fixture at the Amex.
"I looked at the way I thought Tottenham would line up and I selected my team on the back of that," he said.
"Every player still has a chance to play on Saturday, though."