The 28-year-old left English side Essex after one match on Tuesday, just four days after joining to play eight matches in the T20 Bash.
On Wednesday media reports in Bangladesh and Britain said the opener's wife, who wears a hijab, and child had been chased out of a local restaurant and had acid thrown at them.
However, Iqbal said on his Facebook page the reports were "really not true" and said his departure was for "personal reasons".
"England is one my of favourite places to play cricket and Essex have been entirely gracious even though I had to leave early."
Essex refused to comment on the reports and echoed Iqbal's comments.
"Essex County Cricket Club can confirm that overseas player Tamim Iqbal has left the club with immediate effect due to personal reasons," a brief statement read.
The left-hander has scored nine ODI centuries for Bangladesh and eight in Tests.
(Reporting by Neil Robinson; Editing by Alison Williams)
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