The move comes after the Supreme Court partially restored President Donald Trump's executive order that was widely criticised as a ban on Muslims.
The countries named in the order include Iran, Libya, Somalia, Sudan, Syria and Yemen.
The new guidelines sent to US embassies and consulates on Wednesday say that applicants from the six countries must prove a relationship with a parent, spouse, child, adult son or daughter, son-in-law, daughter-in-law or sibling in the US.
Grandparents, grandchildren, aunts, uncles, nieces, nephews, cousins, brothers-laws and sisters-in-law, fiancees or other extended family members are not considered to be close relationships.
The ban will come into effect from Thursday.
The department will continue to "work with the Departments of State and Justice on the way forward for implementation of the executive order based on the Supreme Court's ruling," Department of Homeland Security spokesman David Lapan said.
The Supreme Court on Monday permitted the Trump administration to partially reinstate the travel ban which would affect people from six Muslim-majority countries.
The controversial order was previously struck down by two lower courts.
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