Pradeep, a 25-year-old right-arm bowler, would join the squad soon after his arrival from Zimbabwe on Monday, according to chairman of selectors Ashantha de Mel.
"He has been part of the Sri Lanka A team that took part in the one-day tri-series in Zimbabwe and having played against Pakistan in the recent Test series we thought he will be the most likely replacement," de Mel said.
Pradeep has played his all three Tests against Pakistan but is yet to make his one-day debut.
Kulasekara was ruled out of the series after injuring his groin in the first one-day international at Hambantota which India won by 21 runs on Saturday to go one-up in the five-match series.
The second match is scheduled on Tuesday at the same venue.