CARACAS—Venezuela’s President Nicolás Maduro, struggling with falling approval ratings and a deepening economic crisis, has found what critics say is a convenient scapegoat for his country’s woes: neighboring Colombia.

In recent days, Venezuela deported more than 1,000 Colombian citizens and closed key border crossings in the frontier state of Táchira, where Mr. Maduro declared martial law in several municipalities. The actions were allegedly aimed at cracking down on rampant smuggling of price-controlled Venezuelan goods...