We report clear observations of the magnetic Meissner effect in arrays of superconducting 4 {AA} carbon nanotubes grown in the linear channels of AlPO4-5 (AFI) zeolite single crystals. Both bulk magnetization and magnetic torque experiments show a clear signature of the lower critical Hc1 transition, a pronounced difference in zero-field cooled and field cooled branches during temperature sweeps below 6K, and signatures of 1D superconducting fluctuations below ~15-18 K. These experiments extend the magnetic phase diagram we obtained previously by resistive experiments [Z. Wang et al., Phys. Rev. B 81, 174530 (2010)] towards low magnetic fields and within the range of zero resistance.