Not really. See this from Catholic Answers:
As for the binding force of these documents [Encyclicals] it is generally admitted that the mere fact that the pope should have given to any of his utterances the form of an encyclical does not necessarily constitute it an ex-cathedra pronouncement and invest it with infallible authority. The degree in which the infallible magisterium of the Holy See is committed must be judged from the circumstances, and from the language used in the particular case.
As for the binding force of these documents [Encyclicals] it is generally admitted that the mere fact that the pope should have given to any of his utterances the form of an encyclical does not necessarily constitute it an ex-cathedra pronouncement and invest it with infallible authority.
That is speaking of infallibility, not magisterium. The Ordinary Magisterium is not itself necessarily infallible, and it would be to this authority which most such encyclicals would belong.