Mr Martinelli is accused of using public funds to illegally spy on more than 150 prominent people.
Among those he allegedly spied on are trade union activists, politicians, lawyers, doctors and business people.
Mr Martinelli denied the allegations, saying they were part of a vendetta by current President Juan Carlos Varela.
The court ordered the arrest because Mr Martinelli failed to appear at a hearing earlier this month.
He left Panama in January days before the Supreme Court voted in favour of having him investigated over separate corruption allegations.
He is believed to be living in Miami, Florida.
The court did not give any details about how his detention would be sought.
On Monday, Mr Martinelli tweeted [in Spanish]: "First round of the political trial: without having been properly documented, without charges, without proper notification and without sentence, my provisional arrest has been ordered."
The Supreme Court launched an investigation into the alleged spying ordered by Mr Martinelli in June.
It came after dozens of people alleged they had their phones tapped and that the administration of Mr Martinelli prepared dossiers against them containing intimate information.
Among the alleged victims are high-ranking members of the opposition Revolutionary Democratic Party, as well as lawmaker Jose Luis Varela, who is the brother of current President Juan Carlos Varela.
Investigators said the wiretaps were carried out by members of Panama's National Security Council.
Panama's Supreme Court has ordered the arrest of former President Ricardo Martinelli, who governed the Central American country from 2009 to 2014.