Mahela Jayawardene and Kumar Sangakkara are both IPL players
Sri Lanka's top players will be allowed to appear in next year's Indian Premier League instead of touring England.
Officials say they cannot guarantee to send a full strength side and will now discuss alternative plans with the England and Wales Cricket Board.
"The players were already committed to play in the IPL," said Sri Lanka Cricket chief executive Duleep Mendis.
"They assured us they would give the 2011 tour of England priority ahead of the IPL, so we couldn't let them down."
Earlier this week, Sri Lanka accepted an invitation to tour England and play two Tests and three one-day internationals after the ECB severed sporting relations with Zimbabwe.
But the majority of Sri Lanka's top players are signed up to three-year deals with the IPL's eight team franchises.
The six-week tournament will start on 10 April, and will clash with the first England v Sri Lanka Test, which is scheduled for 8 May.
Mendis added: "We will be taking up the matter with the ECB shortly to find what alternatives we can arrive at without upsetting both parties."
Sri Lanka Cricket hope the tour can be rescheduled, but there is little room for manoeuvre with the ICC World Twenty20 in England starting in June.
If England cannot change dates, then Sri Lanka may offer to send a weakened squad.
Captain Mahela Jayawardene, Kumar Sangakkara, Chaminda Vaas, Muttiah Muralitharan, Dilhara Fernando, Sanath Jayasuriya and Upal Tharanga are among those to have signed lucrative three-year deals with IPL franchises.
And Sri Lanka cricket broadcaster Roshan Abeysinghe told BBC Sport: "13 of their top players have signed up to the IPL, so it will definitely be very close to an A team, which I doubt would be able to give England the type of run a normal Test side would do."
ICC chief executive Haroon Lorgat feels Sri Lanka's decision was inevitable given the financial incentives of playing in the IPL.
In Test cricket you have to play your best side and it appears as though Sri Lanka are not going to do that
Former England captain Alec Stewart
Lorgat told BBC Radio 5 Live: "My folks always used to say money is the root of all evils - at the base of all this is the sums of money involved.
"It's far more attractive to play in the IPL than to come and play in a Test series. Money puts a different spin on a players' affiliations."
Former England captain Alec Stewart feels Sri Lanka must bring their best side for the tour to go ahead.
"It's a big issue and it needs to be looked at by the ECB and, more importantly, the ICC," Stewart told BBC Radio 5 Live.
"We're talking Test cricket, which is meant to be the very best players from both countries playing with and against each other.
"If this isn't going to be the case, they must either move the date or perhaps uninvite Sri Lanka and find someone else.
"This is not the end of it - there will be plenty of discussions taking place but, from my point of view, in Test cricket you have to play your best side and it appears as though Sri Lanka are not going to do that.