Context. The photometric signal we receive from a star hosting a planet is modulated by the variation in the planet signal with its orbital phase. Such phase variations (or phase curves) are observed for transiting hot Jupiters with current instrumentation and have also been measured for one transiting terrestrial planet (Kepler10b) and one nontransiting gas giant (Ups A b). Future telescopes (JWST and EChO) will have the capability of measuring thermal phase curves of exoplanets, including hot rocky planets in transiting and nontransiting configurations and at different wavelengths. Short-period planets with a mass below 10 R⊕ are indeed frequent, and nearby targets (within 10 pc) are already known and more are to be found. Aims: We test the possibility of using multiwavelength infrared phase curves to constrain the radius, the albedo, and the orbital inclination of a nontransiting planet with no atmosphere and on a 1:1 spin orbit resonance. Methods: We modeled the thermal emission of a synchronous rocky planet with no atmosphere and its apparent variation with the orbital phase for a given orbital inclination. We assume that the planet is detected by radial velocity so its orbital period and minimum mass are known. We simulated observed noisy phase curves and then applied an optimization procedure to retrieve the radius and albedo of the planet and the inclination of the orbit. Results: Airless planets can be distinguished from planets having a dense atmosphere and their radius, albedo, and inclination (and therefore true mass) can be retrieved from multiband observations with MIRI-JWST and EChO in the 5-15 μm range. The accuracy depends on stellar type, orbital distance, radius of the planet and inclination: hot and large planets on highly inclined orbit are favored. As inclination above 60° represents half of the randomly oriented orbits, the growing population of short-period, terrestrial-sized planets detected by radial velocity surveys and transits should offer several nearby promising targets for this method, including planets GJ581 e, b, and HD 40307 b. Conclusions: Stellar activity is likely to limit the accuracy of this method, at least for some stars. It has not been taken into account in this study, and its effects will have to be addressed in future works.