Snax 4 U operates from a factory in Keppochhill Place in Springburn in the north of Glasgow.
The firm distributes sandwiches, baguettes and wraps to around 400 premises across the west of Scotland – around 100 of them in Glasgow.
Following yesterday morning's routine inspection the business was shut down.
It is understood more than 3500 items are still in circulation and these have now been recalled.
The products include Snax 4 U own-brand sandwiches, baguettes and wraps filled with tuna, mayonnaise and sweetcorn, cheese and spring onion, cheese and red onion, chicken tikka, chicken tandoori, chicken and sweetcorn, chicken and spring onion, chicken and black pepper.
Snax 4 U branded filled rolls containing tuna, cheese and egg have also been recalled.
Shoppers who bought any of the company's products with a use by date of January 12, 13 or 14 are advised not to eat them but to throw them out or return them to the shop where they were bought.
It is understood the sandwiches are distributed to newsagents and small independent convenience stores.
The Food Standards Agency has asked city council environmental protection staff to keep a look out for any of the affected products when making routine visits to shops.
A council spokesman said: "Environmental health officers found an extensive mouse infestation which they felt constituted a risk to health and that the business should cease trading in order to protect public health."
Council staff slapped a Hygiene Emergency Prohibition Notice on the premises, meaning it had to shut down immediately.
The order has to be ratified by the Sheriff Court within five days.
The spokesman said: "The company cannot trade until they have satisfied us they have dealt with the problem."
Council staff notified the Food Protection Agency, which ordered sandwiches made and distributed by the firm be recalled.
A spokesman for the agency said: "We are working with the relevant local authorities to facilitate an effective recall of products to protect consumers in relation to food safety."