Eleven others were injured when the soldiers opened fire at the mine, in the northwestern region of Sagaing.
Eleven others were injured when the soldiers opened fire at the mine, in the northwestern region of Sagaing, which is controlled by the the military-backed Union of Myanma Economic Holdings Ltd (UMEHL).
The soldiers were thought to be working as security guards at the site, one of dozens of jade mines in the area.
"Yesterday they (UMEHL) warned the freelance miners not to come inside of the site," local lawmaker Maung Tay told AFP.
"But the miners went there this morning and they shot them. There are four miners dead and eleven injured and they are at the hospital now."
The incident comes the same day a screening of a film about the jade industry by Global Witness in Yangon was abruptly cancelled.
Journalists who attended the event at Parkroyal Hotel were read a statement from the hotel saying the corruption watchdog had not gained written permission from the Yangon regional government before the screening.
The film, already available online, explored how Myanmar's military has reaped huge profits from the jade mines in northern Kachin and used them to fuel long-running conflicts with local ethnic groups.
It also called on the government of Aung San Suu Kyi to focus on regulating the jade industry as part of peace talks with armed ethnic groups that are due to start next week.
Myanmar produces the world's finest jadeite, a near-translucent green stone prized in China, where it is known as the "stone of heaven" and believed to bring health and luck.
An investigation by Global Witness found Kachin's mines produced some $31 billion of jade in 2014 alone, equivalent to almost half the country's official GDP that year.
But little of the bounty trickles down to impoverished locals who are left to sift through the rubble left by the mining firms that control the industry -- many of them controlled by military families and drug lords.
Hundreds of itinerant miners are killed by landslides every year searching for gems.
Earlier this month police opened a case against five gem scavengers who discovered a huge jade boulder weighing 8.7 tons in Hpakant, Myanmar's main jade-producing region.