World number 4 Federer, who’s yet to drop a pair at the championship, rescued all seven break points that he faced and won 79 percent of first serve points.
2nd seed Rafael Nadal also reached the final eight years with an easy 6-3 6-4 victory over Filip Krajinovic.
The Spaniard will play with Karen Khachanov following following the Russian’s 6-4 7-6 (7-1) triumph over John Isner.
Edmund, who won the Indian Wells second-tier Challenger event last week, struggled on serve in the opening set.
He had been busted at the very first game of this match and went a double break down, before getting on the plank in 5-1.
The next set has been competitive, with Edmund creating three fracture opportunities as the SWISs served for the match, but he was unable to shoot them.
Federer, a 20-time Grand Slam champion, acquired his 100th ATP name at Dubai at the beginning of March.
In the women’s draw, Canada’s Bianca Andreescu year-old world number one Garbine Muguruza 6-0 6-1 in just 52 minutes to attain on the semi-finals.
The victory sees the 18-year-old reach her third semi final of this year, having beaten Caroline Wozniacki and Venus Williams on her approach into the Auckland Open final in January while she also reached the final four at the Mexican Open at Acapulco fourteen weeks ago.
She’s won 26 of 29 games in 20-19 and will grow in the top 40 of their world rankings next week, despite starting the season 152nd.
Andreescu will play sixth seed Elina Svitolina in the semi-finals after the Ukrainian beat Czech Marketa Vondrousova 4-6 6-4 6-4.
Venus Williams plays Angelique Kerber and Karolina Pliskova meets Belinda Bencic in the Rest of the Quarter Finals on Thursday.
Russell Fuller, BBC Radio 5 Live Tennis correspondent
Edmund made one of the most inauspicious of Start-S his first two service issues were twice faults, and he was defeated smoothly by Federer.
The 20-time Grand Slam champion served typically smoothly, but Edmund didn’t let him run off with matters in the second set, and watched four break-back points stored.
The experience will certainly endure the British number one in good stead in any upcoming meetings, also he has already established a profitable stay in Indian Wells.
He had not won a match all year because of knee problems when he came at the Challenger event, which precedes this Masters tournament. Having won this, and then made a rush to the final 16 of the principal occasion, Edmund has attained confidence and form, as well as standing points.