West Yorkshire Police confirmed this morning that a 25-year-old man from Leeds was in custody and awaiting a mental health assessment.
Officers had received reports that a man had a firearm.
However, police say that no gun has been found.
Officers were called to The Headrow at 9.40pm last night after a number of calls from members of the public.
The man had been seen to enter the Sainsbury’s store in The Headrow prior to his arrest and the store has been closed while a detailed search of the premises is carried out this morning.
Detective Inspector Dave McDougal, of Leeds District CID, said: “We will always treat any report of a person thought to be in possession of a firearm very seriously. Officers responded quickly to these reports and detained the suspect without incident.
“While no firearm was recovered from the arrested man or in initial searches of the area we need to be certain and are conducting further searches today, particularly in the Sainsbury’s store.
“We apologise for any inconvenience this ongoing activity may cause but we hope people will understand that we need to treat reports of this nature seriously. We are aiming to remove the scene as quickly as possible once all necessary searches have taken place.”
Josh Carver, 22, recorded the dramatic moment on his mobile phone while waiting for his fiancé near the store.
He said: “I was waiting to pick up my fiancé just scrolling through Facebook I heard loads of screaming and police cars appeared from everywhere.
“The police then pinned a man down with machine guns.”
Anyone with any information that could assist the investigation is asked to contact Leeds District CID via 101 quoting log number 1731 of February 7.