Ferguson sustained the injury while fielding a ball at practice on Saturday night at the Pallekele Cricket Stadium, with an x-ray later revealing a small fracture to the middle joint.
Coach Gary Stead confirmed Ferguson would return home to New Zealand in the coming days.
"It's a shame for Lockie to have to miss this series, especially coming off the back of such an impressive World Cup campaign in England," Stead was quoted as saying according to a New Zealand Cricket media release.
"The thumb has been put in a splint and is expected to take four to six weeks to recover; so we're optimistic he'll be available for the five-game T20 series against England, which starts on November 1 in Christchurch.
The Black Caps, who have taken a 1-0 lead with a five-wicket win in the first T20I played on Sunday, will face Sri Lanka on Tuesday night.