We present astrometric monitoring data of the binary brown dwarf DENIS-P J1228.2-1547. The data have been obtained with the Hubble Space Telescope over a time span of 5.5 yr, and confirm that DENIS-P J1228.2-1547 is indeed a common proper motion, i.e., physical, binary. The data cover about 1/8th of the binary orbit, indicating an orbital period of ≈45 yr, and a semimajor axis of ≈6.4 AU. A plausible fit of the orbital parameters indicates that both components of the binary are substellar, which is in good agreement with previous mass estimates based on the presence of lithium in the combined spectra of both components. Since the next periastron passage of DENIS-P J1228.2-1547 is expected for the years 2030 to 2035, long-term astrometric monitoring is required to derive accurate mass estimates for the system and the individual components. The photometry obtained with HST/WFPC2 in the F814W band shows no indication for photometric variability with an amplitude larger than 0.05 mag over a time span of ≈1000 days. Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with programmes GO 7952, 8720, 9157, 9345, 9968.