What is the largest country by population that has never won an Olympic medal?

Bangladesh, with an approximate population of 170 million, is the most populous country in the world never to have won an Olympic medal. Bangladesh Olympic Association head Wali Ullah has stated that Bangladesh's weak economy accounts for its poor results in sports.

https://en.wikipedia.org/wiki/Bangladesh_at_the_Olympics

To add to pehinhota's answer...

Until 2016, Bangladesh never had an athlete who had qualified for the Olympics via merit. For the first time, their Rio Flagbearer Siddikur Rahman had qualified for the finals of Golf by coming 55th out of 60 individuals. The country is the most populous nation to have never won a medal in the history of the event despite having had competitors regularly over the past few decades. A majority of the athletes would gain entry into the Olympics via a wildcard system. The focus of Bangladesh has majorly been on cricket with the country only recently beginning to emphasize more on other sports.

https://thebridge.in/olympics-facts/countries-never-won-medal-olympics-20464