A panel heard how PC Katie Babington had drunk "intoxicating liquor" while she was on duty and at a place of work.
A screening breath test reading revealed she was over the limit for police officers on duty.
A further screening, some weeks later, also showed she was over the limit again.
The panel found her conduct amounted to a breach of the standards of professional behaviour in respect of discreditable conduct and fitness for duty.
The hearing, which was held in private earlier this week, heard how PC Babington had already resigned from the force.
A Humberside Police spokesman said: "The allegations were admitted at the level of Gross Misconduct and the Chief Constable determined that had the officer not resigned, then she would have been dismissed without notice."