But he declined to comment on the charges, and would not say if Thaksin would return by the deadline.
Sunai Manomaiudom, the DSI director-general, said police had strong evidence that Thaksin and his wife, Khunying Pojaman, had secretly held shares through nominee companies in SC Asset Corp PCL, a real estate company then owned by the family.
Sunai said they must present themselves to police between June 26 and June 29.
"If he intentionally refuses to come, we will issue an arrest warrant," Sunai said, adding that the case had nothing to do with politics.
Thaksin was ousted in a September coup while he was on a visit to the US and has since lived in London and travelled around Asia.
The order is an about turn by the military-installed government which had previously warned Thaksin not to return for fear he would cause political instability by rallying his many supporters.
As recently as last week, General Sonthi Boonyaratglin, the army commander and coup leader, said Thaksin might be harmed by his enemies if he returned to Thailand.
But Surayud Chulanont, the military-installed prime minister, said on Tuesday that the government would ensure his safety if he returned.
"He has the right to explain and he should be considered innocent for now. I want everything to proceed according to the justice system," he had said.
Thaksin became a billionaire in the telecommunications sector before entering politics and serving as prime minister in 2001-2006.
An anti-graft panel last week ordered about $1.9bn of his assets frozen on suspicion they were gained in an illicit manner.