The unprecedented copper-catalyzed asymmetric alkynylallylic monofluoroalkylation reaction is described via the use of 1,3-enynes and fluorinated malonates. A series of 1,4-enynes bearing a monofluoroalkyl unit are achieved in high yields, excellent regio- and enantioselectivity and high E/Z selectivity. The asymmetric propargylic monofluoroalkylation is also developed. The reliability and synthetic value of the work are highlighted by a gram-scale test and a couple of downstream transformations. Preliminary mechanistic studies unveil a negative nonlinear effect for the catalytic process.