At least 100 others were wounded in the strike, which reportedly struck a warehouse containing weapons.
The commando unit is allied with Houthi rebels whose military capabilities the coalition has been trying to destroy.
Casualties were also reported after air strikes in the northern province of Hajjah, near the Saudi border.
Residents of the Bakeel al-Meer area told the Reuters news agency that at least 40 people had been killed, mostly civilians.
"Houthi gunmen were attacking Saudi border positions from this area but the coalition's planes failed to hit the fighters and bombed civilians [instead]," one resident alleged.
Hours after the air strikes in Hajjah, coalition warplanes targeted the headquarters of the Special Security Forces in the southern Sabaain district of Sanaa.
Officials from the rebel-controlled health ministry said that 36 soldiers and officers had been killed. However, a commando who survived the attack suggested that civilians might also have been among the victims.
"There were many people at the entrance to the warehouse, getting their weapons, farmers, cooks [and also soldiers]; these poor people were standing at the entrance to the warehouse," he told Reuters.
Other air strikes on Wednesday severely damaged a rebel-controlled naval base in the western province of Hudaydah, on Yemen's Red Sea coast.
A rebel-held military base outside Dhalea was also hit, a day after militiamen allied to the exiled government were reported to have taken control of the southern city.
The World Health Organization's director general, Dr Margaret Chan, said on Wednesday that two months of air strikes and fighting on the ground had left up to 2,000 people dead and 8,000 wounded, including hundreds of women and children.
Almost 7.5 million people are in urgent need of medical help.
"Hospitals around the country are closing down their emergency operations rooms and intensive care units due to shortages in staff and fuel for generators," Dr Chan warned. "The health and lives of millions of people are at risk."
The UN has been trying to reschedule peace talks in Geneva that were planned for this week, but the government has insisted the Houthis recognise its authority, withdraw from cities they control and disarm before being allowed to participate.
Saudi-led coalition warplanes have bombed a special forces camp in Yemen's capital, Sanaa, killing at least 36 people, officials and witnesses say.