By Agence France-Presse
Police were investigating if the mine had been laid intentionally or if the victims had accidentally struck unexploded ordnance leftover from a previous conflict, an officer told AFP.
"According to our initial information, it was a homemade mine," the officer said, requesting anonymity.
"It exploded around 10:30am this morning in a field," he said, adding that an elderly man and two boys aged 15 and 17 were killed by the blast.
A 13-year-old boy was hospitalised with injuries.
The north of Rakhine state is an impoverished area scarred by a brutal army crackdown on its Muslim Rohingya population.
The campaign was launched in October in response to deadly raids staged by Rohingya militants, who say they are fighting for political rights for the stateless minority, which Myanmar has been accused of mistreating for years.
The army crackdown has displaced more than 92,000 Rohingya.
The majority fled across the border to Bangladesh, where many gave harrowing accounts of security officers slaughtering babies, burning people alive and staging gang rapes.
The UN has ordered an investigation into the alleged army abuses, saying they may amount to crimes against humanity.
But Myanmar has vowed to block visas for the UN fact-finding team, with de facto leader Aung San Suu Kyi warning that their probe would inflame tensions in the region.
Suu Kyi, a Nobel peace prize winner, has faced global censure for not taking a stronger stance on the Rohingya's plight since coming to power last year.