The Welshman missed Knights' home victory over Hartpury on Saturday after taking ill.
Griffiths, 64, is expected to make a full recovery, according to a statement released today by the Championship club.
'Doncaster RFC (Doncaster Knights) can now confirm that Director of Rugby, Clive Griffiths suffered a suspected heart attack whilst out jogging on Friday evening,' said the statement.
'Clive is currently undergoing tests in Doncaster Royal Infirmary, but is expected to make a full recovery.
'We are sure that everyone concerned with Doncaster Knights, Phoenix and the wider club will want to join us in sending our very best wishes to Clive.'
Former dual-code Wales international Griffiths has had two spells in charge at Doncaster.Â
He returned to Castle Park in 2012 and subsequently guided the club to back-to-back appearances in the promotion play-offs.