Newspapers claimed the 28-year-old's wife was the victim of an attempted acid attack.
His exit from Chelmsford was announced on Tuesday, just four days after he joined Essex for the T20 Blast.
In a post on his Facebook page, Tamim said his decision to return home was taken for "personal reasons".
He continued: "Some media reported that we were the target of attempted hate crime. This is really not true.
"England is one my of favourite places to play cricket and Essex have been entirely gracious even though I had to leave early.
"I thank all my fans and well wishers for their concern and messages, and look forward to going back to England for future matches."
Tamim played only one game for Essex, scoring seven in Sunday's defeat by Kent Spitfires.
"We wish him all the best and it would be appreciated if his privacy is respected," Essex said in a statement on Tuesday.
Bangladesh opener Tamim Iqbal has denied reports a "hate crime" against his family prompted his abrupt decision to leave Essex after just one match.