Bernard Kenny, 77, was stabbed in the stomach as he came to the aid of Mrs Cox when she was attacked outside the library in the centre of Birstall on Thursday.
The former miner was discharged from hospital today, West Yorkshire Police said.
In a statement his family said Mrs Cox’s death was a sad loss for the community, adding: “We would also like to thank people at the scene, the police, ambulance service and the staff at LGI who were excellent in dealing with the situation.
“Finally, many people have shown great kindness over the last few days; this has been much appreciated by the whole family, but now we hope you will respect the fact that we need time and privacy for Bernard to recover.”
Mr Kenny is understood to have been part of the rescue teams which helped at the Lofthouse Colliery disaster in 1973.
Seven men died when part of the now-closed pit near Leeds flooded.
An online petition has been set up calling on the Government to award Mr Kenny the George Cross - the highest bravery honour that can be given to non-military personnel.
On Monday morning, it had been signed by more than 3,000 people.
The message, directed at Cabinet Office minister Matthew Hancock, says: “During the vicious, hellish attack on MP Jo Cox, an elderly gentleman by the name of Bernard Kenny tried to defend her.”
It adds: “We believe that Bernard Kenny deserves the highest honour for bravery that this country can award. The Cabinet Office must make it so as quickly as possible, so that our nation’s thoughts are on love and bravery rather than hate and fear.”
Mr Kenny’s actions were remembered at church services on Sunday when congregations prayed for his recovery.
Parishioner Leif Wickes led prayers at St Peter’s Church in Birstall, West Yorkshire, close to where the pensioner lives with his wife, Doreen.
Mr Wickes said that Mr Kenny “despite his 77 years intervened in the attack to try and save Jo’s life and was stabbed and badly injured”.
He said: “We give thanks for his courage and his example and pray for his speedy recovery.”