The officers were patrolling in the Beckmill Court area of town when they saw the trio acting suspiciously at the back of a shop.
The suspects ran off and after a foot chase all three men were arrested nearby.
The men - two are aged 18 and the other 21 - remain in custody today (Monday) and are being questioned on suspicion of burglary (other than dwelling).
Police have been carrying out operational activity in the town in response to a number of burglaries at commercial properties since December.
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Det Sgt Jon Putnam said: “Our efforts to stop those involved in these offences in their tracks continues in the area.
“Local businesses in Melton have been hit hard by the Covid pandemic, and at a time when they should have been preparing for the Christmas and New Year trade, some were instead clearing up after being targeted by unscrupulous thieves.
“The local neighbourhood team are working hard to disrupt these burglaries and deal positively with those who are committing them.”
And in a message to shop owners and staff in Melton he added: “Our advice to local retailers would be to remove charity boxes and cash floats to secure locations out of view overnight, as these items seem to be a potential target for thieves.”