Limits on additional planetary companions to OGLE 2005-BLG-390L

10 pages, 4 figures, accepted by A&AInternational audienceAims. We investigate constraints on additional planets orbiting the distant M-dwarf star OGLE 2005-BLG-390L, around which photometric microlensing data has revealed the existence of the sub-Neptune-mass planet OGLE 2005-BLG-390Lb. We specifically aim to study potential Jovian companions and compare our findings with predictions from core-accretion and disc-instability models of planet formation. We also obtain an estimate of the detection probability for sub-Neptune mass planets similar to OGLE 2005-BLG-390Lb using a simplified simulation of a microlensing experiment. Methods: We compute the efficiency of our photometric data for detecting additional planets around OGLE 2005-BLG-390L, as a function of the microlensing model parameters and convert it into a function of the orbital axis and planet mass by means of an adopted model of the Milky Way. Results: We find that more than 50% of potential planets with a mass in excess of 1 MJ between 1.1 and 2.3 AU around OGLE 2005-BLG-390L would have revealed their existence, whereas for gas giants above 3 MJ in orbits between 1.5 and 2.2 AU, the detection efficiency reaches 70%; however, no such companion was observed. Our photometric microlensing data therefore do not contradict the existence of gas giant planets at any separation orbiting OGLE 2005-BLG-390L. Furthermore we find a detection probability for an OGLE 2005-BLG-390Lb-like planet of around 2{-}5%. In agreement with current planet formation theories, this quantitatively supports the prediction that sub-Neptune mass planets are common around low-mass stars