The properties of ultracompact dwarf (UCD) galaxy candidates in Abell 1689 (z = 0.183) are investigated, based on deep high-resolution images from the Hubble Space Telescope Advanced Camera for Surveys. A UCD candidate has to be unresolved, have i < 28 mag (MV < -11.5 mag), and satisfy color limits derived from Bayesian photometric redshifts. We find 160 UCD candidates with 22 mag < i < 28 mag. We estimate that about 100 of these are cluster members, based on their spatial distribution and photometric redshifts. For i ≲ 26.8 mag, the radial and luminosity distribution of the UCD candidates can be explained well by Abell 1689's globular cluster (GC) system. For i ≲ 26.8 mag, there is an overpopulation of 15 ± 5 UCD candidates with respect to the GC luminosity function. For i ≲ 26 mag, the radial distribution of UCD candidates is more consistent with the dwarf galaxy population than with the GC system of Abell 1689. The UCD candidates follow a color-magnitude trend with a slope similar to that of Abell 1689's genuine dwarf galaxy population, but shifted fainter by about 2-3 mag. Two of the three brightest UCD candidates (MV ≃ -17 mag) are slightly resolved. At the distance of Abell 1689, these two objects would have King profile core radii of ≃35 pc and reff ≃ 300 pc, implying luminosities and sizes 2-3 times those of M32's bulge. Additional photometric redshifts obtained with late-type stellar and elliptical galaxy templates support the assignment of these two resolved sources to Abell 1689 but also allow for up to four foreground stars among the six brightest UCD candidates. Our findings imply that in Abell 1689 there are ≥10 UCDs with MV < -12.7 mag, probably created by stripping "normal" dwarf or spiral galaxies. Compared with the UCDs in the Fornax Cluster - the location of their original discovery - they are brighter, larger, and have colors closer to normal dwarf galaxies. This suggests that they may be in an intermediate stage of the stripping process. Checking the photometric redshifts of the brightest UCD candidates with spectroscopy would be the next step to definitely confirm the existence of UCDs in Abell 1689.