Citing own work within a paper and being anonymous I am reading a paper in which the author cites his paper in a very explicit form. The reformulation of one of his sentence in the paper was in this form: 


  I have already made this point in a few papers, within a general
  framework in (Some Name) (1996) and in a related 
  framework in (Some Name) (1999).


This paper is submitted to a peer-reviewed journal. With this sentence, the author gives an explicit information about his identity and becomes non-anonymous to referees. By the way, he is a well-known guy in his literature.

Is it an acceptable situation ? 

ps. I edited the question in order to avoid a confusion. I am just reading the paper and I wanted to know, by curiosity, how a such situation is considered in academia.
If this is in the context of double-blind reviewing, the correct response to this situation is to alert the handling editor or PC chair to this situation. Different venues are differently strict about double blind reviews, so the response to the situation may vary between "well, we don't care if the authors wants to reveal himself" to a reject and resubmit (without the incriminating statement and a new set of reviewers). However, which of those it is is not your decision as a reviewer.

If this is not in the context of double-blind reviewing, you are aware of the identity of the authors anyway, and this statement gives you no additional information.

If you are just reading the paper (and not reviewing), as implied by the wording of your question, then I don't understand the issue. Published papers generally have publicly visible authors, and it is not clear that the incriminating wording was already visible during review. For instance, in many software engineering venues that nowadays use double-blind reviewing, it is customary to "blank" self-citations and to slightly change the phrasing for the review version to make sure that identities are not, or at least not obviously, revealed. This can then be changed back for the camera-ready version.