Sweden's The Local said Thursday that even Archbishop of Canterbury Rowan Williams declined the invitation to Sunday's ceremony for Eva Brunne, who was appointed in May to be bishop of the Church of Sweden Stockholm Diocese.
The bishops from England and Northern Ireland said the ceremony was at odds with Anglican rules.
"The Anglican Church has a moratorium right now concerning the ordination of bishops who live together with someone of the same sex," said Alan Harper, a bishop from Armagh in Northern Ireland.
Officials of the Swedish church said they did not consider the lack of attendance to be a "boycott" and had not expected Rowan to attend in any case.
Sweden earlier this year gave same-sex marriages the same legal status as heterosexual unions.