The ultraviolet (1250-1950 A) energy distribution of the X-ray burst source 4U/MXB 1735-44 has been observed with the International Ultraviolet Explorer. The source was detected with an average flux of 1.1 x 10 to the -15th ergs/sq cm per sec per A. The similarity of the optical energy distribution of this source to that of Sco X-1 extends into the far-ultraviolet. Assuming that the optical and ultraviolet emission of MXB 1735-44 is due to reprocessing of X-rays in an accretion disk, the ratio of X-ray to bolometric (optical + ultraviolet) flux has been used to make an estimate of the thickness of the disk. For an assumed X-ray albedo of 0.5, it is found that the disk extends to less than approximately 6 deg from the orbital plane.