The 25-year-old was randomly tested during the recent Pakistan tour of Sri Lanka and the results of his urnine samples returned positive, Sri Lanka Cricket (SLC) said in a statement.
The first Test begins on December 10.
"SLC has been advised that a sample provided by Kusal Janith Perera for a random testing carried out by the ICC during the recent Pakistani tour, has yielded a positive result for a banned substance," said the SLC statement.
"In view of this and in terms of the applicable ICC Regulations, SLC has recalled Perera from New Zealand. SLC will take all steps required to have a further sample tested and make every endeavour to enable Kusal Janith Perera to resume playing cricket at the earliest opportunity in compliance with the ICC Regulations."
"ICC confirms @OfficialSLC Kusal Perrera provisionally suspended after a sample he provided was found to contain a prohibited substance," the International Cricket Council (ICC) said on Twitter.
ICC confirms @OfficialSLC Kusal Perrera provisionally suspended after a sample he provided was found to contain a prohibited substance.
— ICC Media (@ICCMediaComms) December 7, 2015
Perera will be replaced by right-hand batsman Kaushal Silva.
The wicketkeeper-batsman was to play in the two-match Test series starting in Dunedin on December 10 and the following One-day International series.
He became the second Sri Lankan international cricketer after Upul Tharanga to be found positive for a banned substance. Tharanga, the left-handed opener served a three month ban following the 2011 World Cup.