The 25-year-old will now miss Saturday's Gloucester game but McCall said it was too early to say whether the latest injury will affect the player's chances of making the England tour of South Africa in June.
"There are two and a half weeks until the (playoff) semi-final, so all things considered it's probably best he doesn't play this weekend," McCall BBC 5 live.
"If anyone has a hamstring tightness on Wednesday, it wouldn't be the most sensible thing to play him (on Saturday).
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"Maybe having not played rugby for a long time, these kind of things can happen quite easily."
Vunipola remains in contention to return for Saracens' playoff semi-final against either Wasps or Newcastle Falcons on May 19.
His wretched injury run, including shoulder and knee issues, has kept him out of England duty since early last year.
England captain Dylan Hartley, centre Jonathan Joseph, lock George Kruis and winger Anthony Watson have been ruled out of Eddie Jones' squad for three tests against the Springboks in June.
Bath have also urged England not to consider flanker Sam Underhill as he continues to recover from a foot injury.
(Reporting by Hardik Vyas in Bengaluru; Editing by Amlan Chakraborty)
