Involved in folate metabolism. Catalyzes the irreversible conversion of 5-formyltetrahydrofolate (5-FTHF) to yield 5,10-methenyltetrahydrofolate (By similarity). (6S)-5-formyl-5,6,7,8-tetrahydrofolate + ATP = 5,10-methenyltetrahydrofolate + ADP + phosphate Monomer or homodimer. Belongs to the 5-formyltetrahydrofolate cyclo-ligase family.