Selvarajah Jayanthan, 39, an LTTE member between 1996 and 1998, was the prime suspect in the shooting.
Justice M Illancheliyan was unhurt while his personal protection officer was injured when an unknown gunman fired on his car on Saturday. Officer Sarath Premachandra succumbed to his injuries on Sunday.
Sirisena ordered the police probe into the assassination attempt on the Tamil high court judge and called for a special programme to strengthen the security of judges in the country.
It was not immediately known if the suspect was a rehabilitated LTTE cadre. Two others are already in police custody.
More From This Section
The government said that after the end of the military campaign in 2009, over 11,000 LTTE cadres were rehabilitated and integrated into society.
The judge called the shooting as an attempt on his life.
The incident caused protests in the north yesterday with members of the judiciary boycotting courts.
It was said that the suspect had grabbed the revolver belonging to the judge's advance motorcycle outrider, the police sergeant who died in the incident.
He had presided over the trial in high profile rape and murder case of young student Sivaloganathan Vithya. The incident, which took place in May 2015, had caused much public outrage.