In a report to the Ministry of Industry and Trade on Thursday, the department cited recent violations by the two platforms and provided screenshots as evidence.
Vietnam caps discounts at 50% of a product or service.
The department emphasized the need for stricter penalties, such as blocking ads or suspending operations for repeat offenders.
It also urged for increased supervision of international e-commerce platforms to maintain a fair business environment and safeguard consumer rights.
It also proposed perfecting the legal framework to avoid tax losses on these platforms.
Temu began allowing Vietnamese consumers to shop on its platform last month but has not registered in the country.
Singapore-based Shopee is the biggest e-commerce platform in Vietnam with more than 71% of market share in the second quarter, according to e-commerce intelligence firm YouNet ECI.