Those arrested - 15 women and four men in their early 20s - were detained on Sunday at an event center in the city where the wedding was taking place, Lawan Ibrahim Fagge told AFP.
"Our men stormed the venue where a gay couple was having a wedding and arrested 19 men and women, including the female organizer of the wedding," he said.
He said the would-be couple had escaped but police have launched a manhunt for their arrest.
Fagge said the suspects had been remanded in custody pending further investigation.
Kano is among around a dozen predominantly Muslim states in northern Nigeria where sharia law operates alongside common law.
Homosexuality is punishable by death under that law, although the sentence has never been enforced.
In 2014, Nigeria passed legislation outlawing same-sex marriages and the promotion of civil unions.
The law prescribes up to 14 years in jail for anyone confirmed to be in a same-sex union.
The sharia police, known as the Hisbah in Kano, has raided several lesbian and gay weddings in the city and made arrests but no one has been convicted.
In January 2015, the Hisbah also arrested 12 young men at a popular resort on the outskirts of the city for allegedly planning a gay wedding but the suspects insisted they had gathered for a friend's birthday party.
In 2018, the Hisbah rounded up 11 young women for allegedly planning a lesbian wedding.
The suspects, who said they belonged to a dance club, denied the allegation, saying they organized the party to celebrate the appointment of one of them as the club's deputy head.