Class I methanol masers are known to be associated with shocked outflow regions around massive protostars, indicating a possible link between the maser properties and those of their host clumps. The main goals of this study are (1) to search for new class I methanol masers, (2) to statistically study the relationship between class I masers and shock tracers, (3) to compare the properties between class I masers and their host clumps, also as a function of their evolutionary stage, and (4) to constrain the physical conditions that excite multiple class I masers simultaneously. We analysed the 3mm wavelength spectral line survey of 408 clumps identified by the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL), which were observed with the IRAM 30-meter telescope, focusing on the class I methanol masers with frequencies near 84, 95, and 104.3GHz. We detect narrow maser-like features towards 54, 100, and 4 sources in the maser lines near 84, 95, and 104.3GHz, respectively. Among them, 50 masers at 84GHz, 29 masers at 95GHz, and 4 rare masers at 104.3GHz are new discoveries. The new detections increase the number of known 104.3GHz masers from five to nine. The 95 GHz class I methanol maser is generally stronger than the 84 GHz maser counterpart. We find nine sources showing class I methanol masers, but no SiO emission, indicating that class I methanol masers might be the only signpost of protostellar outflow activity in extremely embedded objects at the earliest evolutionary stage. Class I methanol masers that are associated with sources that show SiO line wings are more numerous and stronger than those without such wings. The total integrated intensity of class I methanol masers is well correlated with the integrated intensity and velocity coverage of the SiO (2-1) emission. The properties of class I methanol masers are positively correlated with the bolometric luminosity, clump mass, and peak H_2 column density of their associated clumps, but are uncorrelated with the luminosity-to-mass ratio, dust temperature, and mean H_2_ volume density. We suggest that the properties of class I masers are related to shocks traced by SiO. Based on our observations, we conclude that class I methanol masers at 84 and 95GHz can trace a similar evolutionary stage to the H_2O maser, and appear prior to 6.7 and 12.2GHz methanol and OH masers. Despite their small number, the 104.3GHz class I masers appear to trace a shorter and more evolved stage compared to the other class I masers.