West Indies were 20-1 when rain stopped play on Saturday, and the covers remained on the field throughout the following day at the P. Sara Oval.
The umpires finally cancelled play at 2:45pm local time (0915 GMT) following an inspection of the rain-soaked pitch.
Shai Hope was on 17 when rain stopped played on Saturday, leaving the visitors a target of 244 to win the second Test and level the two-match series.
The West Indies have not won any of their 10 previous Tests played in Sri Lanka since their first in 1993.
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