About 13,000 people attended the first Hull Street Food Nights in April in Trinity Square.
Organisers said police told them to relocate the monthly event to Zebedee's Yard because "there were too many access points for a vehicle to be driven at speed" into the plaza.
Police stressed there had been no specific threat to the event itself.
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They said public safety was their main priority.
More than 20 people were killed when 22-year-old Salman Abedi carried out a suicide bomb attack at Manchester Arena on 22 May.
Eight people were killed in the London Bridge attack on 3 June and five killed in the Westminster attack on 22 March.
The current national threat level is severe, which means an attack is highly likely.
Kathryn Shillito, city centre manager of event organisers Hull BID (Business Improvement District), said: "Post-Manchester and London, and in consultation with the police, safety and security was paramount so on taking their advice, we relocated the event to Zebedee's Yard and Princes Dock Street."
She said the move would mean a bigger festival with more stalls.
The organisation said there would be security checks of bags at various entry points to the festival, including Princes Dock Street, Whitefriargate, Dagger Lane and Posterngate.
In a social media post, it said: "Really sorry for any inconvenience but we're sure you'll appreciate that with the recent tragic events - and after consulting with the police - security has to be tight.
"All we ask is for people to be understanding and patient and we'll get everybody through as soon as we can.
"We've put in so much hard work to make this event happen and just want it to be safe, and for our visitors to have a fantastic time. Thank you."
Fears over a potential terror threat have forced a food festival in Hull to be relocated to another city location.