Eyewitnesses report that the 41-year-old mother of two was left lying bleeding on the pavement after the incident.
She was subsequently airlifted to Leeds General Infirmary. Her condition is reported to be critical and serious.
West Yorkshire Police said they were aware of an incident in relation to an assault on the MP.
The force said in a tweet: “We are aware of a serious incident ongoing in Birstall. Details will be released in the press in due course.”
Witness Daniel Blyth, 38, a company director from the town, told the Yorkshire Post newspaper that the assault was “unusual”.
“I saw seven police cars racing up Leeds Road towards Morley. They were unmarked BMWs,” he said.
“There are two helicopters flying overhead. It all seems very dramatic. I have heard that two people have been shot but I’m not who are why. It’s all very unusual for Birstall.”
Eyewitnesses told Sky News the assailant appeared to be using an adapted replica or homemade gun.
Ms Cox chairs the All Party Parliamentary Group on Syria and is currently a backbencher.
She was elected in 2015 and previously served on the Communities and Local Government Select Committee.
A number of MPs have been subject to assaults while going about their work in recent years.
East Ham MP Stephen Timms was stabbed twice during a constituency surgery at a library in May 2010. The attacker, Roshonara Choudhry said she had been influenced by Al Qaeda and that her attack had been in revenge for the Iraq War.
Mr Timms suffered potentially life-threatening wounds but recovered and continued as an MP.
Un January 2000, Cheltenham MP Nigel Jones was injured in an attack at his local office by constituent Robert Ashman with a samurai sword. That MP’s assistant, local councillor Andrew Pennington was killed in the attack.
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