Alonso, who is third overall in the F1 championship, clocked a time of 1 minute, 18.482 seconds. Hamilton was .419 seconds behind and four-time defending champion Sebastian Vettel was .535 behind for Red Bull.
Spectators waited for nearly 40 minutes as drivers stayed in their garages as the damp track dried after some rain showers.
Hamilton was fastest in the first morning session ahead of Mercedes teammate Nico Rosberg and Red Bull driver Daniel Ricciardo.
There is a final practice session Saturday morning before qualifying in the afternoon.
Hamilton, who has won 26 races, has never started from pole in Monaco.