This work presents the first high-precision variability survey in the field of the intermediate-age, metal--rich open cluster NGC 6253. Clusters of this type are benchmarks for stellar evolution models. Continuous photometric monitoring of the cluster and its surrounding field was performed over a time span of ten nights using the Wide Field Imager mounted at the ESO-MPI 2.2m telescope. High-quality timeseries, each composed of about 800 datapoints, were obtained for 250,000 stars using ISIS and DAOPHOT packages. Candidate members were selected by using the colour-magnitude diagrams and period-luminosity-colour relations. Membership probabilities based on the proper motions were also used. The membership of all the variables discovered within a radius of 8 arcmin from the centre is discussed by comparing the incidence of the classes in the cluster direction and in the surrounding field. We discovered 595 variables and we also characterized most of them providing their variability classes, periods, and amplitudes. The sample is complete for short periods: we classified 20 pulsating variables, 225 contact systems, 99 eclipsing systems (22 Beta Lyr type, 59 Beta Per type, 18 RS CVn type), and 77 rotational variables. The time-baseline hampered the precise characterization of 173 variables with periods longer than 4-5 days. Moreover, we found a cataclysmic system undergoing an outburst of about 2.5 mag. We propose a list of 35 variable stars (8 contact systems, 2 eclipsing systems, 15 rotational variables, 9 long-period variables and the cataclysmic variable) as probable members of NGC 6253. ; Comment: Astronomy and Astrophysics, in press. Extended version with tables and light curves