"Fifteen people including seven civilians were martyred", the statement said.
The army truck was passing by Quetta's Pishin Stop area of the city when it was targeted by the explosion.
It said incendiary explosives were used and that the bomb started fires in nearby vehicles. Following the blast, officials have declared an emergency in the city, reported the Dawn news.
It is not yet clear if it was a suicide attack or a planted bomb.
The Chief of Army Staff (COAS) General Qamar Javed Bajwa condemned the terrorist attack and said that such terror-inducing attacks can not shatter our hopes.
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There was no immediate claim of responsibility for the blast.
Sarfraz Bugti, the home minister for Baluchistan, said the blast took place near a private hospital. "Our resolve won't succumb to any challenge", Maj Gen Asif Ghafoor tweeted.
Inter Services Public Relations (ISPR) confirmed that at least 15 people including eight security forces' personnel embraced martyrdom while 25 others were injured in the blast in which a security forces' vehicle was targeted. Attacks have also been reported by groups related to the Taliban.
Mineral-rich Balochistan, where Gwader is located, has been plagued for decades by a separatist insurgency and sectarian killings.
The ISPR said the vehicle deployed on security duty was targeted in the attack. Police placed a cordon around the area and were collecting evidence. However, military intelligence officials denied the Wadh network exists and the father of the alleged leader says his son is not involved with militants attacking the state.