WASHINGTON—The Trump administration is banning immigration from Nigeria, Africa’s most populous nation, and three other countries in an expansion of its policy blocking travel from seven other nations.

Under a proclamation signed Friday by President Trump, citizens from Nigeria, Eritrea, Myanmar and Kyrgyzstan won’t be allowed to apply for visas to immigrate to the U.S. The Trump administration said the policy was designed to tighten security for countries that don’t comply with the U.S. minimum security standards or cooperate...