"The donations died quickly when this service came into effect," says Red Cross press spokesperson Karin Tengby to Swedish Television.
She believes it creates confusion and that it is more difficult for users to give money since they must register with the service first.
"Many want to donate money to us, but it should be easy. Right now, it's not," she says.
Tengby says that while customers have to register to buy bus tickets or give to charity, they do not have to if they want to vote in tv shows, such as the Eurovision Song Contest. The charity now wants a similar exemption from the scheme.
"They don't use WyWallet and the text message just costs ten crowns."
WyWallet is a payment system or "mobile wallet" that is owned by Sweden's big four mobile operators, Telia, Tele2, Telenor and 3. WyWallet is available to 97% of the country's mobile phone users and supports P2P money transfers, SMS transit and ticketing payments, online shopping and prepaid card top-ups.