People are being asked to get tested even if they have no symptoms, have already had Covid or have already been vaccinated - anyone who tests positive will be told to isolate for 10 days.
The testing will be carried out in the following areas:
Clayton & Fairweather Green
Thornton & Allerton
The Bradford West MO Naz Shah told ITV News that she was worried that Bradford could be put under local restrictions if the variant, now known as Delta, isn't brought under control.
According to the latest government data the case rate per 100,000 in Bradford is 54.7, which is above the national average but is lower than areas such as Kirklees where surge testing is already taking place.
In a letter to Naz Shah MP, Imran Hussain MP and Judith Cummins MP the Health Secretary, Matt Hancock, said: "It is right that we act with caution towards variants of concern, as it is vital that we don’t allow a variant to undo all of the hard work and sacrifices that the vaccine rollout is doing to protect people.
"The first line of defence is to spot and suppress variants of concern aggressively wherever they’re found."
He also urged people to get vaccinated if they were eligible and to get tested whether they have symptoms or not.
It has not been said how many cases of the so-called Indian Variant have been discovered in the borough or how long the surge testing will take place.
Bradford Council Leader, Cllr Susan Hinchcliffe, said: "While additional testing is underway, everyone is being asked to be extra vigilant for any COVID 19 symptoms.
"As with any variant of COVID-19, the guidance remains the same and we must all continue to regularly wash your hands, use face coverings when appropriate, keeping your distance from others when outside your house, and ventilate rooms with fresh air."