We present the first polarimetric space very long baseline interferometry (VLBI) imaging observations at 22 GHz. BL Lacertae was observed in 2013 November 10 with the RadioAstron space VLBI mission, including a ground array of 15 radio telescopes. The instrumental polarization of the space radio telescope is found to be less than 9%, demonstrating the polarimetric imaging capabilities of RadioAstron at 22 GHz. Ground-space fringes were obtained up to a projected baseline distance of 7.9 Earth diameters in length, allowing us to image the jet in BL Lacertae with a maximum angular resolution of 21 mu as, the highest achieved to date. We find evidence for emission upstream of the radio core, which may correspond to a recollimation shock at about 40 mu as from the jet apex, in a pattern that includes other recollimation shocks at approximately 100 and 250 mu as from the jet apex. Polarized emission is detected in two components within the innermost 0.5 mas from the core, as well as in some knots 3 mas downstream. Faraday rotation analysis, obtained from combining RadioAstron 22 GHz and ground-based 15 and 43 GHz images, shows a gradient in rotation measure and Faraday-corrected polarization vector as a function of position angle with respect to the core, suggesting that the jet in BL Lacertae is threaded by a helical magnetic field. The intrinsic de-boosted brightness temperature in the unresolved core exceeds 3 x 10 super(12) K, suggesting, at the very least, departure from equipartition of energy between the magnetic field and radiating particles.