MEXICO CITY — In a country of limits, it is the restriction that many Cubans hate the most: the exit visa that the government requires for travel abroad but rarely grants, trapping most Cubans looking to leave even for just a few days.

Now that bureaucratic barrier is on its way out. The Cuban government announced Tuesday that it would terminate the exit visa requirement as of Jan. 13, letting many Cubans depart for vacations, or forever, with only a passport and a visa from the country where they plan to go.