Hundreds of women in the German city were subjected to sexual assaults on New Year's Eve, 2015.
Jess Phillips, Labour MP for Birmingham Yardley, said it was akin to "heckling" on Birmingham's Broad Street.
Mrs Phillips made her comments on Thursday's BBC Question Time.
She was speaking during a debate about how many refugees should be allowed into Britain, in which an audience member suggested events in Cologne - said to have been carried out by migrants - proved mass immigration did not work.
She told the audience: "A very similar situation to what happened in Cologne could be describing Broad Street in Birmingham every week, where women are baited and heckled."
But viewers took to social media to reject the comparison.
Chris Humphreys tweeted: "Did Jess Phillips just compare the apparent mass sexual assault in Cologne with Birmingham city centre? Oh dear oh dear."
James Wilby said of the comments: "They are quite insane. And an example of a feminist hiding from reality."
Harry Yorke said the comparison of the Cologne attacks to Broad Streets was "utter tripe and disingenuous".
The comments also angered Mike Olley, who looks after Broad Street in his role as manager of the Westside Business Improvement District.
He said: "It's preposterous, ill-informed nonsense actually. It's a throwaway line from someone who hasn't got as much of a grasp as people - particularly myself - who work in the area."
Mrs Phillips finished her statement on the programme by saying: "We have to attack what we perceive as being patriarchal culture coming into any culture that isn't patriarchal and making sure we tell people not to be like that.
"But we should be careful in this country before we rest on our laurels when two women are murdered every week in this country."
An MP has been criticised for downplaying the Cologne sex attacks by comparing them to harassment of women during a typical night out in Birmingham.