Broady was downed 6-1 6-1 by the Croatian, who is ranked 38 in the world.
Broady won the first game of the match, but things went badly after that as second-seed Martic reeled off 11 games in a row.
Swiatek sweeps past Svitolina to secure Gauff semi-final in Rome
The British number four lost in just 56 minutes.
Barty powers past Kudermetova to reach Rome quarter-finals
Anett Kontaveit upsets top seed Petra Martic to set up Fiona Ferro final in Palermo