Three simultaneous bombings hit security checkpoints in the coastal city at sunset, just as troops fasting during the holy Muslim month of Ramadan were breaking their fast, said the security official.
That was soon followed by a fourth bombing at the entrance of an army camp, he said, adding that in all "17 soldiers as well as a woman and child passing by were killed".
The attacks were all carried out by suicide bombers, the source told AFP.
The Pentagon revealed last month that a "very small number" of US military personnel had also been deployed around Mukalla in support of the operation, led by special Saudi and Emirati forces.
The US Navy has several ships nearby, including an amphibious assault vessel, the USS Boxer, and two destroyers.
Al-Qaeda in the Arabian Peninsula, based in Yemen since 2009, and the Islamic State group have exploited the power vacuum created by the conflict in Yemen to expand their presence in the south and southeast.
