Indika and Mendis have been suspended by Sri Lanka Cricket pending an ICC investigation.
Sri Lanka's three-Test series with England begins on Tuesday.
According to the ICC statement, Zoysa has been charged with breach of article 2.1.1, 2.1.4 and 2.4.4.
Zoysa faces charges of attempting to fix or otherwise influence improperly the result or other aspects of an worldwide match, of soliciting fellow professionals to do the same, and for failing to disclose any approach by potential fixers to the ICC Anti-Corruption Unit.
The report also added that another Sri Lanka coach lower down in the organisation is also expected to be charged soon.
He played his last worldwide match in 2007 and later worked in India with the Goa Cricket Association as a fast-bowling coach.
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Sri Lankan Cricket, in confirming Zoysa was on indefinite leave, said it had started commissioning a "fully-fledged anti-corruption unit" and was seeking the ICC's help.
Last month, Zoysa's former captain and teammate, Sanath Jayasuriya, was charged over his failure to cooperate in their investigation.
It is understood the charges relate to trying to recruit members of the current Sri Lanka team to fix upcoming matches.
Nuwan Zoysa, a former global who played 30 Tests and 95 ODIs from 1997-2007, has 30 days to respond to three charges from the ICC's anti-corruption unit.
SLC also suspended provincial coach Jeevantha Kulathunga in the same case.
Zoysa has never worked with Sri Lanka's senior national team.
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