A bank robber was caught red-handed — literally — yesterday after a rookie Brooklyn cop approached him because smoke was wafting from his shirt, police said.

Officer Carlos Corporan was heading to the 90th Precinct station house in Williamsburg at 2 p.m. when he spotted Terence Buckley, 47, trailing a cloud of smoke.

Corporan thought Buckley fit the description of a crook from a Brooklyn Heights robbery that day and told him to stand against a wall.

Then a red dye pack exploded in Buckley’s pocket just as Corporan heard a radio call of a robbery at a nearby Chase branch, cops said.

Buckley was charged with robbery and possession of stolen property in that heist.