The council believes the takeover would directly threaten the future of the Ospreys, removing them from the professional tier and ending men’s regional rugby in Swansea.
The WRU has stated its intention to reduce the number of professional men’s regions in Wales from four to three, with the Ospreys on borrowed time should Y11 complete the purchase of Cardiff.
Council leaders are seeking an urgent court hearing, which they say could take place as early as this week.
However, the authority has indicated that proceedings could be delayed if the WRU provides a written undertaking confirming it will not complete the deal in the interim.
A Swansea Council spokesperson said: "The proposed deal between the WRU and Y11 to buy Cardiff Rugby would mean the end of the Ospreys as a men's professional regional rugby team playing in the URC.
"We are seeking an injunction to prevent this deal going ahead so that further discussions can take place while the current four-team regional structure remains in place.
"The injunction would give all parties the opportunity to consider other options for the future of regional rugby in Wales.
"We believe this is a reasonable and proportionate action given the risk to the future of the Ospreys and the impact that would have on Swansea and the wider region.
"Players, supporters, residents, community clubs and local businesses stand together in support of the Ospreys remaining as one of Wales's four professional regional rugby sides."
The decision to pursue legal action was taken by the council’s cabinet on Monday and received cross-party backing.
The authority has also underlined its wider commitment to the Ospreys, including plans to redevelop St Helen’s as the club’s future home.
In parallel with the court application, the council has also formally requested an investigation by the Competition and Markets Authority.
That submission raises concerns about the proposed reduction in professional teams, the method by which licences would be allocated, and the implications of a single ownership group potentially controlling two Welsh clubs.
The WRU is yet to comment on the injunction application and the council’s latest move as the dispute over the future shape of professional rugby in Wales intensifies.
