A highly efficient heterogeneous copper(I)‐catalyzed three‐component coupling of terminal alkynes, diazoesters and aldehydes has been achieved by using 10 mol% of copper(I) iodide complex [N,N‐CuI‐MCM‐41] anchored on 2‐aminoethylamino‐modified mesoporous material MCM‐41 as the catalyst under mild conditions, delivering a wide variety of 2‐alkoxycarbonyl‐substituted (E)‐1,3‐enynes in mostly good to high yields with excellent stereoselectivity. The heterogenized copper(I) complex can be facilely prepared from inexpensive reagents by using a simple procedure and exhibits a remarkably higher catalytic activity than CuI, and can be recycled more than ten times without a significant drop in its catalytic efficiency. This protocol represents the first example of heterogeneous copper‐catalyzed stereoselective construction of functionalized 1,3‐enynes from simple and commercially available starting materials.