The Samoa-born player hobbled off the field after 15 minutes of the 25-18 win over Ulster on Saturday.
Tuilagi was making only his second start after three weeks out with a groin problem but Leicester said it was not a recurrence of the same injury.
"Manu has had a scan and we’re still waiting for an exact prognosis and timescales - but it will certainly be a few weeks," Leicester Tigers head coach Richard Cockerill told Sky Sports television.
He ruled out a return in November to ensure the player does not suffer any injury set backs.
"We're working with England and their medical team to make sure we get the right diagnosis and the right treatment to get him on the field as quickly as we can.
"Manu is a very powerful athlete and we need to get him exactly right before he goes back on the field. It is a big season for him and England with the World Cup (next year)," said Cockerill.
England host New Zealand on Nov. 8 before taking on South Africa, Samoa and Australia on subsequent weekends.
(Editing by Alan Baldwin)
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