The family are demanding 300,000 kronor ($42,600) in compensation for the pastor’s unruly behaviour.
The service was held a few weeks ago in north-western Skåne.
A report sent by the family to the Church of Sweden states that the priest was noticeably drunk, wobbly on his feet and was forced to prop himself by clutching on to the altar.
He went on to read a poem that no one in the congregation could understand, according to an article in newspaper Helsingborgs Dagbladet.
The sozzled pastor was also reported to have been behaving inappropriately with a younger woman in attendance, kissing her hand and hugging her in a manner unsuitable for a man of the cloth.
The family is currently pursuing their 300,000 kronor claim with the church.
“It’s considerably less than what we have paid in church taxes,” they said.