According to the always-reliable Wikipedia, this is a machlokes. R' Elyashiv recommends participating in a seudas mitzva, and thus, breaking the fast early, in order to avoid this problem.
There is some discussion among the poskim (halakhic authorities) regarding whether a firstborn born through caesarean section is required to observe this fast, given that he is not obligated in the Redemption of the Firstborn. The Chok Ya'akov (470:2) suggests that such a firstborn may be required to fast, while the Kaf HaChayyim (470:3) rules that he need not fast. To circumvent this question, as well as [the] dispute regarding a firstborn non-Jew who converts to Judaism, Rabbi Yosef Shalom Elyashiv ([Ha]Seder Ha'aruch, Vol. 3, p. 44) suggests that such firstborns participate in a seudat mitzvah
H/T to Michoel for pointing out a flaw in the Wiki article, and to Fred (probably) for correcting it.