A leading prosecutor on Tuesday said police detained the three on suspicion of involvement in the blast that struck the heart of the country's security forces in Sistan-Baluchestan.
"Due to security reasons, I am not giving the details of their names, but these terrorists are Iranians," Mohammad Marziah, the prosecutor in Zahedan, the provincial capital, told Iran's Fars news agency.
Authorities are also seeking a man who accompanied the suicide bomber, Marziah said.
Fifteen members of Iran's elite Revolutionary Guards were among those killed in the attack, which struck ahead of a meeting between Revolutionary Guards commanders and tribal chiefs.
Throngs of uniformed mourners paid their respects for the dead at a funeral on Tuesday in Tehran, Iran's capital.
A Sunni rebel group, Jundollah, has claimed responsibility for the attack, but Iranian authorities have accused Pakistan of having links to the bombers, a charge Pakistan denies.
Manouchehr Mottaki, Iran's foreign minister, said members of the group accused of mounting the attack regularly criss-cross the frontier with Pakistan."Members of this terrorist group regularly violate the border and launch attacks inside Iran," he said, without naming the group.
"They cross into Iran illegally. They are based in Pakistan."
Major-General Muhammad Ali Jafari, the head of Iran's Revolutionary Guards, has named the prime suspect behind the bombing as Abd ul-Malik Rigi - who is believed to be based in Pakistan.
Jafari said Tehran would send a delegation to Islamabad to deliver "proof to them so they know that the Islamic Republic is aware of Pakistan's support".
He also expressed his belief that US and British intelligence services were involved and that there would "have to be retaliatory measures to punish them".
But a Pakistani foreign ministry spokesman has rejected the claim.
"Pakistan is not involved in terrorist activities ... we are striving to eradicate this menace," he said.
Washington has also denied involvement with the group, which it has labelled as a "terrorist" organisation, and has condemned the attack.
Source: Al Jazeera (English)