The magnetoconductance of p-n junctions formed in clean single wall carbon nanotubes is studied in the geometry where a magnetic field is along the tube axis. For long junctions the low temperature magnetoconductance is anomalously large; the relative change in the conductance becomes of order unity even when the flux through the tube is much smaller than the flux quantum. The magnetoconductance is negative for metallic tubes. For semiconducting and small gap tubes the magnetoconductance is nonmonotonic: positive at small and negative at large fields. The identified magnetoconductance mechanism is relevant to magnetotransport in undoped metallic and small gap tubes in the presence of a long range disorder potential.