Only 38 overs were played, and the better part of two sessions lost.
The West Indies resumed on 113-6 in reply to Sri Lanka's 386 and rallied in the morning through overnight batsmen Kyle Mayers and Jason Holder, who added 50 to their partnership.
They combined for 63 before Mayers was caught on 45 by Sri Lanka captain Dimuth Karunaratne off spinner Dhanajaya de Silva.
Holder was out for 36, caught by Dushmantha Chameera at point off left-arm spinner Praveen Jayawickrama, leaving the tourists 175-8.
Rakheem Cornwall and Joshua da Silva led West Indies to lunch, but in the fifth over afterwards, Cornwall mistimed a pull at a short ball by Suranga Lakmal and top-edged it to square leg.
He made a valuable 39 from 58 balls with five boundaries and a six over midwicket to raise the team's 200.
Cornwall and da Silva combined for 49, their team's second best partnership.
The rain arrived at that moment and never really left, but the umpires waited for 3 1/2 hours.
More rain is forecast on days four and five.
If and when play resumes, Sri Lanka can take the new ball.
Da Silva was 11 not out from 70 balls with Jeremy Solozano next man in to make his test debut.
Spinners Praveen Jayawickrama and Ramesh Mendis have taken three wickets apiece.