Police arrested Pelta and two officials from the Education and Sports Ministry in May and charged them with abuse of power, breaching fiduciary duties and favouritism in public tenders.
"FACR confirms that a resignation from the post of the chairman was delivered on Monday," spokesman Michal Jurman said in a statement.
Czech media reported Pelta was accused of providing undue benefits when handling state subsidies for 2017 worth 454 million crowns (£15.1 million).
Pelta, 52, has denied any wrongdoing. He has chaired the association since 2011.
FACR held a meeting to replace him last Friday but failed to elect a successor, keeping Pelta in place.
The association has struggled with corruption and match fixing allegations in the past, with several managers and players receiving sentences, but never a sitting chairman.
The Czech side, currently placed third in Group C behind holders Germany and Northern Ireland, plays Norway on Saturday in their next qualifier for the 2018 World Cup. The Czechs last played at the world's top tournament in 2006.
(Reporting by Robert Muller; Editing by Angus MacSwan)
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