Muralitharan, out of Test cricket since August last year, was expected to make a comeback during the tour which was postponed from January due to the Asian tsunamis which ravaged Sri Lanka on December 26.
But the 32-year-old, who underwent corrective surgery last month, was unlikely to be fit in time to play the two Test matches in Napier (April 4-8) and Wellington (April 11-15), Clarke said.
"Murali's shoulder is still stiff," the physiotherapist said. "He will start rehabilitation and bowling again around March 17 but the New Zealand tour is unrealistic."
The off-spinner claimed a world record 532 victims in 91 Tests before the injury, but was later surpassed by Australian leg-spinner Shane Warne who has so far grabbed 566 wickets in 120 Test matches.
The Sri Lankan, who is getting married to an Indian girl later this month, has also been contracted to play County cricket for Lancashire during the first half of the English summer.
But Clarke declined to confirm if Muralitharan will be able to play in England from the last week of April.
"His suitability for England depends on the rehabilitation period," Clarke said.
Muralitharan played his first international match since August when he turned out for an Asian XI against a World XI in the tsunami charity One-dayer at Melbourne in Australia in January.
But doctors ordered a minor surgery on the right shoulder when the pain resurfaced after the match.
Sri Lanka are expected to name their New Zealand-bound squad on Tuesday.