A magnesium base alloy pipe having high strength and toughness is provided along with a method of manufacturing such pipes. A magnesium base alloy pipe, wherein the pipe is produced by drawing a pipe blank of a magnesium base alloy comprising containing either of the following ingredients (1) or (2): (1) about 0.1-12.0 mass % of Al; or (2) about 1.0-10.0 mass % of Zn and about 0.1-2.0 mass % of Zr. The novel alloy pipe is manufactured by a method comprising steps of providing the above-described pipe blank, pointing the pipe blank, and drawing the pointed pipe blank. The drawing step is executed at a drawing temperature above approx. 50° C.