Second seed Murray has spent seven hours and 14 minutes on court against Radek Stepanek and Mathias Bourgue.
Davis Cup captain Leon Smith says Murray's good form before Roland Garros may be behind his initial struggles.
"If it doesn't quite go that way in the early rounds here, there's a bit of frustration," Smith said.
Murray's meeting with big-serving veteran Karlovic is the second match on Court Suzanne Lenglen on Friday at approximately 11:00 BST.
The British number one warmed up for the French Open by beating world number one Novak Djokovic in straight sets in the final of the Italian Open.
But, by his own admission, Murray has been well short of that level so far in the French capital. He posted an image of a Get Out of Jail Free card from the board game Monopoly on social media after fighting back from two sets to one down against world number 164 Bourgue.
Smith, who was also a childhood coach of Murray's, says the 29-year-old could rediscover his form as suddenly as it left him.
