Gibraltar was admitted as a provisional member of European football's governing body on Monday and a decision on whether to grant full membership will be taken at a UEFA Congress in London next May.
Wert, whose portfolio also includes education and culture, said Gibraltar's provisional membership meant it could not yet take part in UEFA competition and said his ministry and the foreign ministry would work to block full membership.
"We have already said we will exhaust all legal means," he told Spanish TV broadcaster Telemadrid.
"I can say that we are reasonably optimistic that this provisionality will not become a definitive acceptance."
Spain claims sovereignty over Gibraltar, which sits at the southern end of the Iberian peninsula at the entrance to the Mediterranean.
The territory - which has an area of about 2.7 square miles and a population of 28,000 - was ceded to Britain under the 1713 Treaty of Utrecht.
Gibraltar's case for UEFA membership has been strengthened by a Court of Arbitration for Sport (CAS) ruling that the governing body must consider its membership.
The territory's government criticised Spain's opposition to it joining UEFA on Monday, saying in a statement that "football and all sport should never be allowed to mix with politics".
"Gibraltar's footballers are ready to excel in international competition and to become the 54th member of UEFA and it is hoped that no further obstacles will be put in their way," the statement added.