A directive from the economy ministry ordered shops to immediately strip shelves of products from Saudi Arabia, the UAE, Bahrain and Egypt.
Inspectors will visit stores to ensure they comply with the order, the ministry said.
The government will also try and stop products such as Saudi dairy goods from entering Qatar via a third country.
Qatar's Government Communications Office (GCO) said it was trying to "protect the safety of consumers".
"Products originating from blockading states, which as a result of the blockade cannot pass the GCC customs territory, has to undergo proper import inspections and customs procedures," the GCO said in a statement.
"Qatar conducts its trade policy in accordance with all of its multilateral and bilateral agreements."
The order comes just days before the anniversary of a bitter Gulf crisis.
Since June 5 last year, Saudi Arabia, the UAE, Bahrain and Egypt have cut all relations with Qatar, accusing it of financing terrorist groups and having close ties with Iran.
The countries subsequently imposed a trade and diplomatic boycott on Qatar, which rejects the charges and says the countries are seeking regime change in Doha.
The row has forced isolated Qatar, which previously relied on its Gulf neighbours, to look elsewhere for food imports, including Turkey, Morocco and Iran.
Many such imports enter the country via ports such as Kuwait and Oman.
It is through these ports, and also via individuals, that goods from the boycotting countries manage to get in to Qatar, said a source with knowledge of the situation.
"Businessmen from the blockading countries are trying to go around the blockade... by using third parties," said the source.
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