Aims. The radiative counterpart of the supermassive black hole at the Galactic center (GC), Sgr A⋆, is subject to frequent flares that are visible simultaneously in X-rays and the near-infrared (NIR). Often, enhanced radio variability from centimeter to sub-millimeter wavelengths is observed to follow these X-ray/NIR eruptions. We present here a multi-wavelength campaign carried out in April 2009, with the aim of characterizing this broadband flaring activity. Methods. Concurrent data from the XMM-Newton/EPIC (2–10 keV), VLT/NACO (2.1 μm, 3.8 μm), APEX/LABOCA (870 μm), and Fermi/LAT (0.1–200 GeV) instruments are employed to derive light curves and spectral energy distributions of new flares from Sgr A⋆. Results. We detected two relatively bright NIR flares, both associated with weak X-ray activity, one of which was followed by a strong sub-mm outburst  ~200 min later. Photometric spectral information on a NIR flare was obtained for the first time with NACO, giving a power-law photon index α =  −0.4 ± 0.3 (Fν ∝ ν   α). The first attempt to detect flaring activity from the Fermi GC source 1FGL J1745.6–2900 is also reported. We model NIR, X-ray, and sub-mm flares in the context of non-thermal emission processes. We find that the simplest scenario involving a single expanding plasmoid releasing synchrotron NIR/sub-mm and synchrotron self-Compton X-ray radiation is inadequate to reproduce the data, but we offer suggestions to reconcile the basic elements of the theory and the observations.