Jamal Kiyemba, a Ugandan, was arrested with the the help of US officials in the capital on Tuesday, police added.
Prosecutor Joan Kagezi was shot dead on 30 March, a day before the trial of men accused of involvement in bombings.
Mr Kiyemba, a former UK resident, was freed from Guantanamo Bay in 2006 without being charged with any offence.
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He was arrested in Pakistan in 2002 for alleged links with al-Qaeda, and later transferred to the controversial US-run detention centre in Cuba.
"There was an operation which we carried out with our counter-terrorism team because we suspect that Jamal Kiyemba and his colleagues have been involved in some form of criminality," Ugandan police spokesman Fred Enanga told Associated Press news agency.
There was no conclusive evidence to link him to Ms Kagazi's killing, but he was being questioned about his possible role in her murder and in other crimes, he added.
Gunmen on a motorbike shot dead Ms Kagezi in a suburb of Kampala.
She was prosecuting 13 men accused of being linked to suicide bombings which killed 76 people in Kampala in 2010.
The US deported Mr Kiyemba to Uganda after the UK refused to take him back.
He had lived in the UK for eight years before travelling to Pakistan.
US President Barack Obama has promised to shut the Guatanamo Bay detention centre because of concerns of widespread human rights abuses.

Joe Storey, 27, had denied murdering Kerri McAuley, 32, who was found dead at Southalls Way, Norwich, on 8 January, but admitted manslaughter.
Storey was high on cocaine when he punched mother-of-two Ms McAuley after a row about an ex-girlfriend.
The jury at Norwich Crown Court took less than an hour to find Storey guilty. He will be sentenced on Friday.
The court had heard friends describe a history of domestic violence which left Ms McAuley "disfigured" and fearing for her life.
In her texts Ms McAuley described Mr Storey's behaviour as "not normal". She wrote: "you are not ready to care for anyone but yourself".
"You were trying to kill me, you were suffocating me until I nearly passed out", adding that if he stays away "hopefully you won't go to prison for beating me to a pulp".
Later Mr Storey and Ms McAuley agreed to meet up again.
Pathologist Dr Benjamin Swift said in the fatal attack Ms McAuley sustained multiple facial lacerations and one of her ears was torn.
Dr Swift said some of the injuries were caused by "blunt force impact".
Storey, of Murrells Court, Norwich, had admitted the pair had a turbulent relationship.
He said he was staying at Ms McAuley's home when she confronted him about his ex-girlfriend who she thought was back in contact with him.
Storey said he struck her five or six times and had a phone in his hand at the time but insisted he had "not to hit her with it".
Prosecutor Simon Spence said Storey behaved like an animal and if "he'd had a scrap of humanity" Storey would have called an ambulance after the attack instead of leaving Ms McAuley to die in the flat.

The 23-year-old, whose brother Sam has returned to the Rabbitohs after a spell in rugby union, said in May that he was keen to play in the NFL.
Jarryd Hayne, another National Rugby League player, left Parramatta Eels to join the San Francisco 49ers this year.
It is understood the Giants hold weekly trials, and that Burgess was one of many to take part on Thursday.
Burgess, born in Dewsbury, West Yorkshire, began his career at Super League side Bradford Bulls, but only spent two seasons there before moving to NRL club Rabbitohs where he joined his brother Sam and twin George.
The England international was part of the Rabbitohs side that beat St Helens 39-0 to win the 2015 World Club Challenge.
An ex-Guantanamo Bay detainee has been arrested in Uganda for questioning over his possible role in the killing of a top prosecutor, police say.
[NEXT_CONCEPT]
A man has been found guilty of murdering his "on-off partner" by bludgeoning her to death.
[NEXT_CONCEPT]
South Sydney Rabbitohs prop Tom Burgess has had a trial with the New York Giants American football team.