The recent discovery of massive black holes ( BHs ) in the centers of high-mass ultra compact dwarf galaxies ( UCDs ) suggests that at least some are the stripped nuclear star clusters of dwarf galaxies . We present the first study that investigates whether such massive BHs , and therefore stripped nuclei , also exist in low-mass ( M < 10 ^ { 7 } M _ { \odot } ) UCDs . We constrain the BH masses of two UCDs located in Centaurus A ( UCD 320 and UCD 330 ) using Jeans modeling of the resolved stellar kinematics from adaptive optics VLT/SINFONI data . No massive BHs are found in either UCD . We find a 3 \sigma upper limit on the central BH mass in UCD 330 of M _ { \bullet } < 1.0 \times 10 ^ { 5 } M _ { \odot } , which corresponds to 1.7 % of the total mass . This excludes a high mass fraction BH and would only allow a low-mass BHs similar to those claimed to be detected in Local Group GCs . For UCD 320 , poorer data quality results in a less constraining 3 \sigma upper limit of M _ { \bullet } < 1 \times 10 ^ { 6 } M _ { \odot } , which is equal to 37.7 % of the total mass . The dynamical M / L of UCD 320 and UCD 330 are not inflated compared to predictions from stellar population models . The non-detection of BHs in these low-mass UCDs is consistent with the idea that elevated dynamical M / L s do indicate the presence of a substantial BH . Despite not detecting massive BHs , these systems could still be stripped nuclei . The strong rotation ( v / \sigma of 0.3 to 0.4 ) in both UCDs and the two-component light profile in UCD 330 support the idea that these UCDs may be stripped nuclei of low-mass galaxies where the BH occupation fraction is not yet known .