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The three men shot Mrs McAliskey, formerly known as Bernadette Devlin, in the chest, arm and thigh as she went to wake up one of her three children.
Her husband, Michael, was also shot twice at point blank range.
Three men are now being questioned by police. They were arrested by members of the Parachute Regiment, who were on patrol nearby when they heard the shots.
The McAliskeys were flown by army helicopter to hospital in Belfast, where their condition is said to be serious, but not life-threatening.
Loyalists blamed
Police say it was a professional attack. The gunmen cut the telephone wires to the house, before breaking down the front door with a sledgehammer.
Loyalist paramilitaries are being blamed for the attack.
Mrs McAliskey has played a leading role in the campaign for Republican prisoners in the Maze, who are demanding "prisoner of war" or political status. They want to be held separately from loyalist supporters in the Maze.
Four other members of the campaign for the H-block inmates have been murdered.
Seven Maze prisoners went on hunger strike before Christmas in support of their demands for political status.
The strike was called off on 12 December after Irish Prime Minister Charles Haughey convinced the inmates their families wanted them to start eating again.
In Context
Bernadette McAliskey was the youngest-ever woman MP when she was elected at the age of 21 in 1969. She served as the Independent Unity member for Mid Ulster from 1969-73.
As an MP, she continued to champion the cause of catholics in Northern Ireland. She was imprisoned for her part in the sectarian riots in Londonderry in August 1969, which led to the deaths of five people and the deployment of troops in the province.
After her marriage in 1974 she faded from public view until her involvement in the H-block campaign.
In October 1993, she gave evidence to a court in San Francisco on behalf of James Smyth, who escaped from the Maze in 1983. He was fighting the British government's attempts to extradite him.
More recently, Mrs McAliskey fought the extradition of her daughter, Roisin, to Germany, where she is wanted for questioning about the IRA bombing of the Osnabruck base in 1996.
Roisin's extradition to Germany was blocked in March 1998 by the Home Secretary, Jack Straw, on medical grounds.