Prosecutors claimed in their motion the photo was posted after defense attorney Don West's tense cross-examination with prosecution witness Rachel Jeantel last week.
The caption in the photo posted by West's daughter reads "We beat stupidity celebration cones" and "dadkilledit."
Prosecutors said an inquiry was necessary "to ensure that witnesses and court proceedings are treated with respect and not as occasions for inappropriate jokes."
West said in a court filing Tuesday that the ice cream photo was taken a day before Jeantel testified and has nothing to do with her testimony. He called the prosecution's motion "irresponsible" and said he had nothing to do with the posting of the photo or its caption.
West said he has stopped for ice creams each night since the trial started and he was joined by his daughters a week ago. They decided to capture the moment with a photo because one of his daughters lives out of town, he said.
"It was not taken for any such purpose or in any way as a comment on anything having to do with the case," West said in the filing. "To me it was a private moment with my family. My daughter accepts responsibility for her immature and insensitive comment and apologizes for it.
Jeantel was talking to Trayvon Martin on the phone moments before he was fatally shot by George Zimmerman last year. She is considered a star witness for prosecutors.
Zimmerman pleaded not guilty to second-degree murder, claiming he shot Martin in self-defense.