The magnetization of iodine intercalated Bi 2 Sr 2 CaCu 2 O 8 (I + Bi-2212) single crystal has been measured as a function of magnetic field H and temperature T. The extracted fluctuation part of the magnetization exhibits a critical behavior consistent with the three dimensional XY model. The static critical exponent v is 0.99 +/- 0.1, which is increased from the value 0.77 +/- 0.1 for pristine Bi-2212, indicating that the weak interlayer coupling along the c-axis of iodine intercalated Bi-2212 significantly increases the static critical exponent v. This result supports that Bi-2212 has an increased static critical exponent v that is larger than the value of 0.669 of YBa 2 Cu 3 O 7 - χ (YBCO) single crystal.