Mr Horomia, 62, has been MP for Ikaroa Rawhiti since 1999 and was minister of Maori affairs from 2002 to 2008.
"The whanau is very humbled by all the love, support and kind wishes for their grandfather, father, brother and uncle," his family said in a statement on Monday.
"Parekura is at home in Mangatuna with his whanau, convalescing. They would appreciate privacy at this time."
A Labour Party spokesman told NZ Newswire the party was aware of the statement.
"Our thoughts are with Parekura at this time," the spokesman