The incident came just two days after the two countries reaffirmed their adherence to a ceasefire to end a brief armed conflict.
The army's statement said the incident took place in Thailand's Sisaket province and "clearly demonstrates to both domestic and international society that the use of concealed weapons in border areas continues to exist, constituting a clear violation of the Ottawa Convention by the Cambodian side".
The Ottawa Convention, also called the Anti-Personnel Mine Ban Treaty, is an international agreement banning the weapons' use, and both Thailand and Cambodia have committed to it.
A statement from Thailand's foreign ministry said the incident confirmed the Thai army's findings "that new land mines are being laid in blatant violation of international law."
It also noted this was the third such incident in less than a month.
Five days of armed conflict broke out last month, killing dozens of people on both sides, including civilians, and displacing more than 260,000.
The fighting broke out a day after five Thai soldiers were wounded when one tripped an anti-personnel mine in disputed territory.
A ceasefire that took effect on July 29 ended major fighting, though tension remained high.
The two countries, on Thursday, at a meeting in Malaysia, committed to a 13-point agreement on implementing their truce.
The Thai army statement, citing its spokesperson, Major General Winthai Suvaree, charged that Saturday's mine explosion constituted "a significant obstacle to the implementation of ceasefire measures and peaceful resolution of problems".
A statement issued in response by the Cambodian Mine Action and Victim Assistance Authority denied Thailand's allegation that Cambodia had laid new mines.
"We have not, and will not, plant new land mines," said the statement, noting that Cambodia is a party to the Anti-Personnel Mine Ban Treaty Convention, "and has an internationally recognised record of removing, not deploying, these indiscriminate weapons".
It noted that Cambodia has cleared more than one million mines and nearly three million other pieces of unexploded ordnance left over from more than three decades of war and civil unrest that began in 1970.
Cambodia had suggested that the two earlier explosions last month, which wounded Thai soldiers, might be land mines from past conflicts.
Tensions had simmered since May this year when a Cambodian soldier was shot dead by Thai troops in a brief fracas in another contested border area.
The escalating dispute was marked by border crossing restrictions and cross-border boycotts and bans on goods and services before fighting broke out.
In Saturday's incident, a Thai sergeant major suffered severe injuries, including losing his left foot, said the Thai army statement, while two privates suffered lesser injuries.
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