A method and system for enabling MMS message delivery to a recipient device. An MMSC receives and stores MMS message content to be delivered to the recipient device, and the MMSC responsively sends to the recipient device an MMS-notification message carrying an address of the MMS message content stored at the MMSC and then receives a reply indicating that the recipient device received the MMS-notification message. The MMSC then detects that, after the MMSC received the reply, (i) at least a predefined threshold amount of time has passed and (ii) the MMSC has not yet received from the recipient device a request to download the MMS message content. And responsive to at least the detecting, the MMSC then sends to the recipient device a data-service-trigger message that triggers turning on data service of the recipient device, thus enabling MMS-message delivery to the recipient device.