Nigeria's top health official, Abdulaziz Abdullahi, told the AFP news agency that the country had received 100,000 face masks, 1,000 protective gowns and 20,000 test kits.
The equipment will be distributed to frontline health workers and hospital laboratories, he said.
Ma, the founder of e-commerce giant Alibaba, has vowed to donate equal amounts of gear to all 54 countries in Africa.
He has also offered the United States half a million test kits and a million masks.
Also on Wednesday, Nigeria's army chief Lieutenant General Tukur Brutai opened a new specialist hospital in Abuja.
He said military medical personnel and equipment would be deployed to fight the disease.
"It is not a coincidence that this facility is coming on stream at this time when coronavirus disease is ravaging the whole world," army medical director Ikechukwu Okeke said at the ceremony.
In a related development, the army also banned large gatherings of its staff while shelving planned events, seminars and other activities.
The army said it would coordinate with other security agencies to enforce restrictions on movement and other government directives.
It promised to "secure all major food stores and government storage facilities of essential goods from looting."
Nigeria has already announced a raft of measures, including travel bans, school and market closures and partial lockdowns in most cities to tame the virus.
Experts are worried about Nigeria's vulnerability to coronavirus because of its huge population and poor healthcare infrastructure. (AFP)