Photographs circulated in online Chinese media this week purported to show a Chinese passport with the words "fuck you" scribbled on two pages next to maps of China and its hotly contested "nine-dash line".
Beijing says the line demarcates its territory in the South China Sea.
But Hanoi, which alongside several other nations has competing claims to the strategically key waters, rejects it.
Earlier this month a UN tribunal said China's line had no legal basis, reviving the acrimony between the two countries.
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Decrying the "shameless and cowardly act" the Consulate General raised the matter with Vietnamese authorities, the statement said, adding "China is outraged" by the incident.
China has demanded Vietnam investigates the alleged act and "seriously punish those responsible", it said, adding "Vietnam has agreed to probe into it".
Vietnamese officials could not be immediately reached for comment.
But earlier this month, state media reported that border authorities in the central city of Danang and southern Phu Quoc island had refused to issue visa stamps on Chinese passports with the nine-dash line.
Others reacted gleefully to an insult to a superpower which is both Vietnam's biggest foreign investor and main regional rival.
One Facebook user wrote "big applause to the immigration officers at Tan Son Nhat" airport, urging border authorities to get their pens out for all Chinese passports.
The reaction is a sign of the enmity between the two countries over the South China Sea.
Hanoi routinely accuses Chinese vessels of sinking Vietnamese fishing boats, while Beijing has built landing strips and other facilities on contested shoals.
But the ASEAN regional bloc soft-peddled the issue at a summit this week despite warnings from Vietnam that the body risks losing relevance if it fails to step up to the security challenge.