The club announced yesterday that the charismatic 64-year-old is undergoing tests at Doncaster Royal Infirmary after suffering a heart attack while out jogging last Friday.
Griffiths, in his second spell at Castle Park after originally joining in 2006, missed Saturday’s 28-17 win over Hartpury in the Championship.
Forwards coach Glen Kenworthy and backs and skills coach Paul Cooke stepped in and will continue to take charge until the popular Welshman makes his return.
De Mulder told The Yorkshire Post: “Clive’s all right. He went jogging last Friday and had a minor heart attack.
“We don’t know what his treatment will be yet and that will decide how long it is before he’s back but the important thing is he’s okay and will make a full recovery.
“I went to see him on Saturday morning and he was fine. In fact, he was still trying to run the show from his bed!
“We had to try and stop him which is difficult as he is so intense when it comes to his rugby. But he’ll need some time now, however long it makes, whether a month or longer.”
Former dual-code international Griffiths has always kept fit and active.
De Mulder added: “Only the other day we were saying how he was bench-pressing the same as one of our younger players – a 26-year-old.
“He was telling us he had the body of an 18-year-old.
“When he’s ready he’ll be back but Glen and Paul ran things very well on Saturday and we have some senior players, too, who will take on more responsibility with the day-to-day stuff.”
Just two games into the new season, Doncaster head to Richmond on Saturday.