Litton, who also missed the opening ODI in Harare, underwent a fitness test on Tuesday but was deemed unfit to return for the remaining two matches.
National team physio Bayjedul Islam Khan said Litton had not made enough progress to be considered for selection.
"Litton had already missed the first ODI and is still not match-fit. He underwent a fitness test today and the outcome was not satisfactory. With back-to-back ODIs coming up, we don't think he will make sufficient progress to play any part in the series," Bayjedul said.
The Bangladesh T20 skipper will now return to Dhaka to continue his rehabilitation.
Left-handed opener Parvez Hossain Emon has been called up as Litton's replacement for the second and third ODIs, scheduled for July 9 and July 11. Bangladesh trail the three-match series 0-1 after losing the opener in Harare.
