The World Cup winner went off at half-time during Tigers' 43-25 defeat against Bath last Saturday.
And while Kay has been ruled out of next weekend's Premiership appointment with Gloucester, he might feature against Harlequins seven days later.
"I affected the nerve in my shoulder in some way which made it difficult to raise my hand above my head properly, which is obviously not right for a lineout jumper," he said.
"There were times in the game when it felt okay, but then other times I was struggling."
Kay will be joined on the sidelines for Gloucester's Welford Road visit by prop Alex Moreno and back-row forward Henry Tuilagi.
Moreno suffered a calf muscle injury during the Recreation Ground warm-up, and left Bath on crutches. He faces a three week lay-off.
Tuilagi, meanwhile, has a hamstring problem and will be absent for at least the next fortnight.
There was better news surrounding England flanker Lewis Moody though, who played the full 80 minutes in Leicester's 22-18 Guinness A League success against Worcester at Sixways on Monday night.
Moody, whose entry to the season was delayed by an arm injury, will now be in contention to face Gloucester.