Perera, 25, failed the test, administered by the International Cricket Council, during the series against Pakistan in late July, Fairfax Media reported.
The Sri Lanka team were not immediately available for comment.
Perera, who played in the tour opener against a New Zealand Board President's XI last week, has been replaced by Kaushal Silva for the test series starting in Dunedin on Thursday.
Sri Lanka Cricket said in the statement that a further 'B' sample would be tested, and it planned to "make every endeavour" to get Perera back on the field as soon as possible.
Pace bowler Dhammika Prasad has also been sent home from the tour after suffering a back injury and has been replaced by Vishva Fernando.
The two-Test series will be followed by five one-day internationals and two Twenty20 matches.
(Reporting by Greg Stutchbury; additional reporting by Steve Tongue; Editing by Ken Ferris)
