The bomb went off in Narathiwat province, one of three Muslim-majority provinces in predominantly Buddhist Thailand where a separatist insurgency has been raging since 2004.
The blast killed a man and his five year-old daughter, the army's Internal Security Operations Command said. The motorcycle was parked opposite the school entrance. Eight people were wounded.
"We suspect this to be the work of people who want to destabilize the situation and cause chaos," the deputy spokesman of the ISOC, Yuthanam Petchmuang, told Reuters.
The attack occurred less than a month after a wave of bombings in tourist towns, including Hua Hin, Phuket and Surat Thani, killed four people and injured dozens.
Police say the tourist-town bombings were linked to the southern insurgency and arrested a suspect over the weekend in connection with the attacks.
Defence Minister Prawit Wongsuwan told reporters on Tuesday that the military government, which took power in May 2014, were making security preparations ahead of the Muslim holiday Eid al-Adha on September 12.
More than 6,500 people have been killed in insurgency-related violence in the Muslim-majority provinces Yala, Narathiwat and Pattani Province since the conflict began, according to Deep South Watch, which monitors the conflict.
While the conflict has been largely confined to the three southern provinces, analysts say that the spread of violence to other provinces could affect Thailand's tourism industry.