I never experienced this. I rarely ever even get the hiccups but this was listed as a symptom when quitting smoking:
Hiccups
Hiccups are reported to be a symptom of nicotine OD, for some people. Because of this, and their common occurrence, they are also known as the 'niccups'. The idea that they may result from an alternative delivery path for the nicotine, via the mouth or gullet (i.e. swallowing it), is attractive to some people.
Hiccups are reported to be experienced by smokers and tobacco users, and are said to be more common among those who use chewing tobacco, Snus, or dissolvable tobacco tablets. It is further suggested that they swallow tobacco juice and hiccups may result. They are not common among pipe and cigar smokers, who are less likely to inhale or swallow smoke, or users of nasal snuff.
Good luck to you and let us know what you do in order to help this issue. It could help others who have experienced the same symptom.