We report muon spin rotation measurements of the temperature dependence and anisotropy of the magnetic field penetration lengths in the heavy fermion superconductor UPt3. We observe a strong axial anisotropy. At 0.05 K we obtain for the penetration length parallel and perpendicular to the c axis lambda(c) = 4260 (150) Angstrom and lambda(a) = 6040 (130) Angstrom, respectively. lambda(a)(-2)(T) at low temperatures excludes a superconducting order parameter in the B phase with only a line of nodes in the equatorial plane of the Fermi surface. The combined analysis of lambda(c)(-2)(T) and lambda(a)(-2)(T) measured in the B phase favours an hybrid order parameter with point nodes at the poles and a line of nodes at the equatorial plane. The A phase is characterized by a larger density of nodes than the B phase.