The FTSE 100 group said the offer from private equity firm Charterhouse Capital fundamentally undervalued the business.
G4S has been under the spotlight recently over a Government probe into outsourcing contracts. It is said to have been under pressure from activist investors to dispose of the cash solutions arm in order to streamline its operations.
But executives insisted that the division, which transports money to ATM machines in high security vans, was key to its plans.
Charterhouse, which bid for the business, already owns high street retailer Card Factory as well as parts of AA and Saga.
Disclosing details of the offer, G4S said: "The board consider the group's cash solutions services to be core to G4S' operations and strategic plans.
"The board regards the nature and timing of the approach to be highly opportunistic and, following due consideration, with the assistance of financial advisers, the offer has been firmly rejected considering the strategic importance of the cash solutions businesses to G4S and because the board believes the conditional offer fundamentally undervalues the business and its prospects."