Foreign Ministry spokesman Le Hai Binh said the airfield, had been "built illegally" on Fiery Cross Reef in the Spratly archipelago, in territory that was "part of Vietnam's Spratlys".
China's Foreign Ministry rejected the complaint, saying that what was a test flight to the newly built airfield on the reef, which China calls Yongshu Jiao, was a matter "completely within China's sovereignty," the Chinese state news agency Xinhua reported.
The United States said it was concerned that the flight had exacerbated tensions.
Washington has criticised China's construction of artificial islands in the South China Sea and worries that Beijing plans to use them for military purposes, even though China says it has no hostile intent.
Pooja Jhunjhunwala, a spokeswoman for the US State Department, said there was "a pressing need for claimants to publicly commit to a reciprocal halt to further land reclamation, construction of new facilities, and militarization of disputed features."
"We encourage all claimants to actively reduce tensions by refraining from unilateral actions that undermine regional stability, and taking steps to create space for meaningful diplomatic solutions to emerge," she said.
Chinese Foreign Ministry spokeswoman Hua Chunying said China used a civil aircraft to conduct the flight to test whether the airfield facilities meet civil-aviation standards.
"China has indisputable sovereignty over the Nansha Islands and their adjacent waters. China will not accept the unfounded accusation from the Vietnamese side," she said, referring to the Spratly's by their Chinese name.
Hua added that China hoped Vietnam could work to achieve "sustainable, healthy and stable" development of bilateral ties.
Hanoi's Foreign Ministry said Vietnam handed a protest note to China's embassy and asked China not to repeat the action.
It called the flight "a serious infringement of the sovereignty of Vietnam on the Spratly archipelago".
China claims almost all the South China Sea, which is believed to have huge deposits of oil and gas, and through which about $5 trillion in ship-borne trade passes every year, and has been building up facilities on the islands it controls.
It completed an airfield on Fiery Cross Reef that security experts say could accommodate most Chinese military aircraft late last year.
Brunei, Malaysia, the Philippines and Taiwan also have rival claims in the South China Sea.