Fast radio bursts (FRBs) are bright radio transients with millisecond duration at cosmological distances. Since compact dark matter/objects (COs) could act as lenses and cause splitting of these kinds of very short duration signals, Muñoz et al. have proposed a novel method to probe COs with lensing of FRBs. In this Letter, we for the first time apply this method to real data and give constraints of the nature of COs with currently available FRB observations. We emphasize that the information from dynamic spectra of FRBs is quite necessary for identifying any lensed signals and find no echoes in the existing data. The null search gives a constraint comparable to that from galactic wide binaries, though the methods of redshift inference from the dispersion measure would impact a little. Furthermore, we make an improved forecast based on the distributions of real data for the ongoing and upcoming telescopes. Finally, we discuss the situation where one or more lensed signals will be detected. In such a case, the parameter space of COs can be pinned down very well since the lens mass can be directly determined through the observed flux ratio and time delay between split images.