Top seed Murray had won the pre-Wimbledon grass-court event in west London twice in the last three years.
Roddick has slipped out of the top 30 in the world rankings after an injury-ravaged campaign, but losing to Roger-Vasselin, ranked 67th, on the grass he regards as his favourite surface is a new low for the American.
Photos: Katrina Kaif, Shamita Shetty at Mumbai airport
Photos: Varun Dhawan, Alia Bhatt promote 'Badri...' on 'Dil Hai Hindustani'
In pictures: 15 facts about kissing that will surprise you
Photos: Shahid Kapoor and Mira Rajput at cafe in Bandra
Photos: Deepika Padukone, Neha Dhupia and Soha Ali Khan at event