A Brooklyn preacher told cops he must have been distracted while eating an ice-cream cone when he fatally mowed down an 88-year-old woman and fled the scene, authorities said yesterday.

Cops eventually nailed Wayne Stokeling, 50, with the help of victim Isabel Rodriguez’s cane — they found evidence of it scratching and denting his BMW from the impact, officials said.

Stokeling had been driving without a license south on Mother Gaston Boulevard in Brownsville when his car struck Rodriguez in the crosswalk at around 8:45 p.m., police said.

Stokeling, pastor of historic St. John’s Baptist Church in Bedford-Stuyvesant, was apprehended by police three blocks away with the help of a witness.

The pastor, who has prior busts for driving offenses, was held in lieu of $200,000 bond.