The 33-year-old man was arrested on suspicion of offences under the Dangerous Dogs Act, West Yorkshire Police said in a statement.
The arrest follows the the death of Emma Bennett who was taken to hospital in a critical condition after receiving serious dog bite injuries in an incident at her home on Monday, police said.
Detective Superintendent Simon Beldon, who is leading the investigation, said: "Early indications are that the two dogs seized from the address are American pit bull terriers although tests are still ongoing to establish their exact make up.
"We are continuing to appeal for anyone with information about the incident or the dogs involved in it to contact the investigation team," he said.
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Bennett, a mother of four, was on a life support machine till she died yesterday.
One neighbour had called 999 after hearing shouts of "no, no, no" coming from her home on Monday afternoon.
Police found her unconscious on the floor of the house with horrendous head and facial injuries. It was feared Emma had suffered brain damage.
Witnesses spoke of "crazy" scenes as up to 30 police officers, including an armed team, descended on the street in Leeds.
One of the pets had escaped from the house but was captured by officers in a road behind the home. The other animal was found in the kitchen, the Mirror reported.
In October, the UK government proposed that owners of dogs that attack and kill people will face 14 years in jail under tough new laws.
According to the proposed rules, if a dog injures someone in an attack its owner could be imprisoned for five years, and if a guide dog is attacked the penalty would be three years in jail.
The proposed changes to the Dangerous Dogs Act came just months after a 14-year-old girl was savaged to death by four dogs while visiting the home of a friend near Wigan, Greater Manchester.