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Colin Duffy, 44, and another man, aged 31, were arrested in the Lurgan area early this morning and have been taken to Antrim Serious Crime suite for questioning, the Police Service of Northern Ireland said.
Mr Black, 52, was gunned down on the M1 motorway early on Thursday as he drove to work at the top security Maghaberry jail near Lisburn, County Antrim.
The father-of-two's car veered off the road and into a drainage ditch after the shots were fired. He was on a stretch of the motorway between Portadown and Lurgan - a dissident republican stronghold in County Armagh.
A Toyota Camry used in the attack was later found burned out in the Inglewood area of Lurgan.
Police have blamed dissident republicans opposed to the peace process for the ambush. They have been engaged in a long-running campaign against conditions in Maghaberry.
Mr Black, from Cookstown, County Tyrone, had served in the Prison Service for more than 30 years and was considering early retirement.
His wife and children are said to be "absolutely devastated" by the killing.
A long-standing member of the Orange Order, Mr Black was the 30th prison officer to be murdered in Northern Ireland since 1974, although the first for almost 20 years.
He was driving his black Audi A4 when the dark blue Toyota drew up alongside and several shots were fired. Police believe he may have already been dead when his car veered off the road.
All sides in Northern Ireland have condemned the shooting, along with Prime Minister David Cameron.
It was discussed at a north-south meeting in Armagh on Friday involving Enda Kenny, Taoiseach of the Irish Republic, Northern Ireland's First Minister Peter Robinson and Deputy First Minister Martin McGuinness.