A troubled Malaysian state investment fund sent at least $850 million last year to an offshore entity set up to appear that it was owned by an Abu Dhabi sovereign-wealth fund, a transfer which deepens the mystery over billions of dollars that are unaccounted for, according to documents reviewed by The Wall Street Journal and people familiar with the matter.

The 1Malaysia Development Bhd. fund, or 1MDB, set up by Malaysian Prime Minister Najib Razak in 2009 to promote economic development, is under investigation in at least...