The state of emergency is in place in Carchi, Pichincha and El Oro provinces, the ministry specified, adding that the measure would last at least until September.
"We reacted in a timely manner. The state of emergency is introduced for the first time to give an effective and substantial response in favor of the people who come to Ecuador," Deputy Foreign Minister Santiago Chavez was quoted as saying by the ministry.
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Venezuela has been struggling with the economic fallout due to a global slump in oil prices and ongoing US sanctions. The May presidential vote resulted in the re-election of President Nicolas Maduro, however, the tensions escalated after a drone attack on the President earlier in August.
According to the European Parliament, over 2 million people have left Venezuela since 2014.