Murhpy has not featured since the goalless draw against Mansfield on March 1 due to a groin complaint.
The 13-goal striker had been taking injections in a bid to get himself fit but manager Wayne Burnett is worried the 23-year-old may be suffering a hernia problem and refuses to rush him back to action.
"Rhys has gone to see another specialist and we'll have a much better idea about the extent of the injury later in the week," Burnett told London 24.
"He's still struggling with it a little bit and they seem to think it may be his hip which is giving him a problem now, but we feel it may well be a hernia.
"Rhys has been having injections and although I want him back, I wouldn't want him to return unless he was 100 per cent. If that's not until the start of next season then that's what it will have to be."
The Daggers sit six points off Sky Bet League Two's top seven with five games remaining.