The incident occurred on Tuesday when the MLA from Jale constituency in Darbhanga, Jibesh Kumar, was on an evening walk.
Forty-four-year-old Kumar was on a phone call when the two men riding a motorbike snatched his iPhone, he told police.
Kumar said that he tried to catch hold of the snatchers but failed.
Nearly three weeks ago, the Ukraine ambassador's mobile phone was snatched near Red Fort in the city. It was recovered within hours.