Pakistan beat Sri Lanka by 113 runs on Sunday to go 2-1 up in the five-match series, with the last two games in Abu Dhabi on Wednesday and Friday.
The International Cricket Council (ICC) said Shehzad pleaded guilty to the offence.
"The opener was found to have breached Article 2.2.4 of the ICC code of conduct for players and player support personnel, which relates to 'inappropriate and deliberate physical contact between Players in the course of play during an international match'," said a ICC statement.
The charge had been laid by the on-field umpires Johan Cloete of South Africa and Pakistan's Shozab Raza, as well as third umpire Richard Illingworth from England and fourth umpire Ahsan Raza of Pakistan.
The incident happened at the end of the 19th over when Shehzad got involved in a debate with Dilshan, which ended with the former pushing the Sri Lanka opener's shoulder.
Shehzad scored a brilliant 81 as Pakistan notched up a massive total of 326-5 in 50 overs before bowling out Sri Lanka for 213 in 44.4 overs.
Pakistan won the first game in Sharjah by 11 runs while Sri Lanka clinched the second in Dubai by two wickets.