A man aged 62 was apprehended by officers after calls came in about someone carrying a weapon at the discount store on Ealing Road in Alperton on April 21.
Emergency services reached the shop at around 4:10 pm following reports of the incident.
The individual was held on suspicion of illegal possession of a firearm and having an offensive weapon with intent to endanger lives.
He continues to be held by police.
According to a spokesperson for the Metropolitan Police, the weapon was not fired and no casualties occurred. The force acknowledged that local residents have been disturbed by what happened and confirmed that extra officers would be deployed to patrol the surrounding streets.