Relevance. Rating Newest Oldest. Best Answer: The minimum fee to send money via Western Union or moneygram is $5. The fee you would have to pay depends on where you are sending the money, where it is being picked up, how much you are sending and how fast you want the money to arrive.elevance. Rating Newest Oldest. Best Answer: The minimum fee to send money via Western Union or moneygram is $5. The fee you would have to pay depends on where you are sending the money, where it is being picked up, how much you are sending and how fast you want the money to arrive.