The April 1 death emerged just as officers launched an annual draft that will see some 100,000 men aged 21 and over conscripted into the military for up two years.
Private Yutthakinun Boonniam, 22, died one day after he was brought to hospital from the army prison in southern Surat Thani province.
Doctors said he suffered kidney failure after a sustained beating by a hard object.
His mother has told local media her son was beaten in the military prison for minor disciplinary offences including oversleeping and missing guard duty.
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"Police have submitted the evidence and names of five army officers and five privates... To ask for arrest warrants against them," Surat Thani's police chief Apichart Boonsrirote told AFP today.
"Based on police's investigation they are involved with the victim's death," he added.
The death is a public relations disaster for the army as draws on young Thai conscripts to fill its ranks.
But rights groups have slammed the incident as the latest example of torture and abuse in the Thai military, which has run the country since a 2014 coup.
"The Thai army faces a chronic inability to end abuses against its conscripts," said Human Rights Watch Asia director Brad Adams, blaming a "culture of impunity".
The watchdog noted that there has been "no progress" in the prosecution of soldiers allegedly responsible for the death of another private in June 2011.
Thailand's military has also been repeatedly accused of extrajudicial killings and torture of civilians.
But the majority of allegations of army abuse and impunity come from the insurgency-torn 'Deep South' of the country, where allegations of killings of unarmed or innocent civilians are rife.
Yet no military personnel have ever been brought to justice over abuses in the southern conflict.