"RC Toulon have decided to launch an internal investigation and could sanction the players if necessary," the French club said in a statement.
"The club use that opportunity to offer their apologies to the Leicester Tigers."
Italian prop Castrogiovanni is under investigation by European Professional Club Rugby (EPCR) after his post-match rant to the media about Leicester's Director of Rugby Richard Cockerill.
Armitage is also being investigated by EPCR after allegedly abusing home fans during Toulon's 25-21 defeat at Welford Road.
Castrogiovanni, a former favourite at Leicester before leaving last May, could face misconduct charges.
The Italian, who has apologised, was reported to have sworn on numerous occasions when talking about the reasons for him leaving Leicester, denying that it had been because of money.
(Reporting by Julien Pretot; Editing by Alan Baldwin)
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