The Dark Blues' first-choice 'keeper, Jack Hamilton, has been ruled out for some time after undergoing surgery to remove his appendix.
Hazard, who was given a straight red card during his last outing for Northern Ireland Under-21s for a shocker of a challenge on Romania's Dennis Man, has experience of playing in Scotland's second tier thanks to loan spells with Falkirk and Partick Thistle.
The 21-year-old, who stands 6ft 6in, will be in Dundee's squad to face Ayr United tomorrow night.
Dens Park boss James McPake told the club's official website, “It’s very frustrating for Jack and the team. He has been fantastic this season and is a big player in our dressing room.
“We have had to act quickly and I’m delighted that we have been able to get someone of Conor’s quality in.
“He is a player who has played in this league over the past two seasons and also has experience of playing at international level.”