Pacheco, belonging to Goa Vikas Party, said he had sent his resignation to the office of Chief Minister Laxmikant Parsekar, now in Bangalore to attend BJP's National Executive.
The Chief Minister's office said Pacheco's resignation was accepted and forwarded it to the Governor.
Pacheco was inducted in state cabinet in November last year after former chief minister Manohar Parrikar moved to the Centre as Defence minister.
Pacheco ran into trouble after the Supreme Court dismissed his petition seeking stay on the conviction order by Goa Bench of Bombay High Court for slapping a government servant on duty in July 2006.
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A Supreme Court bench comprising justices F M I Kalifulla and Shiva Kirti Singh this week dismissed the special leave petition of Pacheco against the July 17, 2014 High Court verdict.
As per the order, he will have to undergo six months imprisonment.
The Goa bench of the High Court had set aside the verdict of a revisional court, which "brought down" the conviction of the MLA under IPC section 323 (causing hurt) from the harsher section 353 (assaulting public servant to deter from duty) and ordered his release on 'admonition' under the Probation of Offenders Act.
The apex court, in July last year,admitted his Special Leave Petition for hearing and exempted him from the surrender to undergo imprisonment.
An FIR was lodged on July 15, 2006 by Kapil Natekar, a junior engineer with state electrical department,alleging that he was abused and slapped by Pacheco in his chamber.
Natekar was called to the minister's office as a telephone call of the latter's personal assistant was not attended a day before the incident.