The country's disaster management agency says hundreds of buildings were damaged by Saturday's tsunami.
It says the possible cause of the tsunami was undersea landslides after the Krakatoa volcano erupted.
The strait, between the islands of Java and Sumatra, connects the Java Sea to the Indian Ocean.
The disaster management agency warned that the death toll after the tsunami, that struck at about 21:30 local time (14:30GMT) on Saturday, is likely to rise further.
Deaths have been reported in the Pandeglang, South Lampung and Serang regions.
Among the areas hit was the popular Tanjung Lesung beach resort in west Java. There was no warning of the advancing wave.