We show that the recent WMAP data can impose a generous upper bound on the effective masses of electron , muon and tau neutrinos defined in the kinematic measurements : \langle m \rangle ^ { 2 } _ { e } + \langle m \rangle ^ { 2 } _ { \mu } + \langle m \rangle ^ { 2 } _ { \tau% } = m ^ { 2 } _ { 1 } + m ^ { 2 } _ { 2 } + m ^ { 2 } _ { 3 } < 0.5 ~ { } { eV } ^ { 2 } , or \langle m \rangle _ { \alpha } < 0.71 eV ( for \alpha = e, \mu, \tau ) . When current neutrino oscillation data are taken into account , we obtain \langle m \rangle _ { e } < 0.24 eV and \langle m \rangle _ { \mu } \approx \langle m \rangle _ { \tau } < 0.24 eV . Thus there is no hope to kinematically detect \langle m \rangle _ { \mu } and \langle m \rangle _ { \tau } in any realistic experiments .