Rafael Nadal, the titleholder and world number two, was equally impressive, crushing Monaco's wild card entrant Jean-Rene Lisnard 6-4, 6-1.
Swiss Federer, who dropped a set against qualifier Novak Djokovic in the first round, played close to perfection, needing just 46 minutes to sweep aside Martin.
"I really can't complain," said Federer, who is starting his claycourt season in the glitzy principality.
"I didn't feel too good against Djokovic but today was just perfect."
The top seed is beginning his warm-up for the highlight of the claycourt season and the only grand slam tournament to elude him, the French Open starting on May 28.
The 24-year-old all rounder will next meet Monaco's Benjamin Balleret, a qualifier who was 4-6, 7-5, 3-2 up against Sebastien Grosjean when the Frenchman pulled out with back pain.
French Open champion Nadal, who started relatively slowly before stepping up a gear to outpower Lisnard, will meet either Belgium's Kristof Vliegen or Czech Jan Hernych.
JOINT FOURTH
The muscular Spaniard has now won 38 consecutive matches on clay which puts him joint fourth on the all-time list led by Argentine Guillermo Vilas with 53 wins in a row.
Monte Carlo Open specialist Guillermo Coria fought back from 5-1 down in the second set to beat Frenchman Paul-Henri Mathieu 1-6, 7-6, 6-4.
The Argentine baseliner has played in the last three finals in the principality and won the Masters Series tournament two years ago.
He struggled in a surprisingly one-sided first set and then lost the first four games of the second. Mathieu served for the match three times but was broken each time by his opponent.
Coria, the 2004 French Open runner-up, survived four match points before taking the second set 8-6 in a tie break.
The combative Argentine stayed on top in the decisive set to edge past Mathieu, who had knocked out former world number one Marat Safin in the first round.
Another Argentine, third seed David Nalbandian, was also made to work before moving past Italian Andreas Seppi, coming back from 5-2 down in the first set to win 7-5, 7-5.
Spain's Juan Carlos Ferrero, who won here in 2002 and 2003, advanced with a 6-1, 6-2 victory over Argentine Juan Ignacio Chela.
(Writing by Patrick Vignal in Paris)
