The supermarket said the "studs" on a ledge outside the Metro convenience store in Regent Street in central London were installed to deter anti-social behaviour like drinking, which intimidated customers.
But with a protest group threatening to demonstrate outside the store, Tesco said it would remove them to address concerns of those who "interpreted them as an anti-homeless measure".
Left Unity called for Tesco to remove the spikes from all stores where they are in place. Spokeswoman Bianca Todd said: "The campaign to remove all the anti-homeless spikes from everywhere they have been put in continues. Homeless people are not pigeons."
A Tesco spokesman said: "Customers told us they were intimidated by anti-social behaviour outside our Regent Street store and we put studs in place to try and stop it.These studs have caused concern for some who have interpreted them as an anti-homeless measure so we have decided to remove them to address this."