The incident followed a weekend of disruptions for the grocer as 14 stores were evacuated around the country on Saturday due to 'unspecified' threats.
The package was blown up at 11.15am this morning, but the Avon and Somerset police force said that the action was taken 'purely as a precaution'.
Store closures over the weekend are thought to have cost the supermarket giant millions of pounds in lost sales.
Police are still investigating the threats towards the stores, but terrorist links have been ruled out.
Earlier today a Tesco spokeswoman said: 'The police are conducting a criminal investigation and Tesco cannot comment further.'