The second day had also been badly affected by heavy showers with only 44.2 overs bowled on Sunday.
In reply to Pakistan's mammoth first innings 551 for six declared, Sri Lanka were 70 for one when play was called off on Monday.
The home team, who need 352 to avoid the follow-on, lost an early wicket in the morning session when Tharanga Paranavitana was dismissed for a duck by Junaid Khan in the two hours of play before lunch.
Paranavitana's opening partner Tillakaratne Dilshan was his usual aggressive self as he hit nine fours in an unbeaten 46. Kumar Sangakkara was 22 not out when the rain came.
The two new-ball bowlers Junaid and Aizaz Cheema bowled some sharp deliveries and beat the bat several times without enjoying much luck.
Earlier, Pakistan batted for 52 minutes to add 63 runs to their overnight 488 for four before declaring.
They lost the wickets of Asad Shafiq for two, run out by a brilliant pick-up and throw by Dilshan, who also caught Adnan Akmal for five from a mistimed cover drive off Rangana Herath.
Pakistan captain Misbah-ul-Haq was left unbeaten on 66, having hit five fours. Abdur Rehman was 18 not out.
Spinner Herath was Sri Lanka's most successful bowler with three for 164.