The 6ft 10in Croat has a serve that should be accompanied by a rumble of thunder. His career has been launched on this missile and Murray must neutralise it to have any hope of progressing.
The portents are good.
The 25-year-old Scot is, at worst, the second best returner of serve in the world. Against Karlovic, Murray will need all his technique, his nerve and, crucially, his reactions.
The last of these attributes has been honed by his penchant for PlayStation games and by playing racket sports as a child, honing co-ordination.
"It is just something I have now and hopefully I will not lose it on Thursday," said Murray. Of his ability with a games console in his hand, Murray said he played regularly with Rafael Nadal and Juan Monaco.
"Most of the tennis players are going to be very good at those sort of things," he said. His favourite game is Goldeneye, with a James Bond theme. Murray will look to terminate Thunderball this afternoon.
The 33-year-old Croat, ranked 59 in the world, poses problems beyond his serve.
"He plays a grass-court game. He likes to come to the net," said Murray. "Someone like Milos Raonic or Kevin Anderson, those sort of guys, play from the back of the court. He's a bit different. It is challenging because it is not about the way you hit the ball against him a lot of the time. It can be down to a couple of passing shots, a couple of reflex shots and also your focus."
Murray's demolition of Nikolay Davydenko on Tuesday was the sign of a player who was in imperious form, striking the ball beautifully and totally demoralising his opponent. The Scot knows this type of performance is unlikely to be repeated against Karlovic because the match-up will make different demands on him.
"You never know when you step on to the court how you are going to play," he said. "The most important thing is that you believe that, no matter what the situation is, you can win the match.
"Against Davydenko, I got ahead and just kept on going. I was in the zone and hitting the ball really well and he wasn't having any chances. The momentum was with me the whole match. I do not expect the same thing to happen against Karlovic. I expect a different match.
"There will be probably be some ups and downs and there will be times when I do not touch the ball for a couple of games on his serve so I am not necessarily going to be in a rhythm in my next match but I have to make sure that mentally I am there for every single point because he can miss a couple of easy volleys and he might serve a double fault.
"I need to be there to capitalise on that as even if I am not playing the best tennis you can still win against him. He has won against the top players and also lost against guys who are ranked 150, 200 in the world. The match can come down to a few points and you need to be there to make the most of his mistakes."
Karlovic, who defeated Dudi Sella of Israel 6-4, 6-4 7-6 (5), is confident he can upset the Scot. Asked if he would upset the Wimbledon crowd today and defeat the world No.4, he said: "Sure."
Murray has defeated Karlovic on the three occasions they met, the last in 2008, but the Croat said he believed he would win because if he did not "I can leave right now home". The words may have been convoluted but his message was unmistakeable.
When asked who were the best players at returning his serve, he said: "I aced everybody."
It is a match that should be compelling even if the rallies are short but it is not yet known whether Judy Murray, the mother of Andy, will be courtside.
The Fed Cup coach has been racing around watching her players and missed her son's thrashing of Davydenko.
"She wasn't there today but it doesn't make a difference," said Murray. "She is here firstly as Fed Cup captain to watch the girls. She also does bits and pieces for radio and then she watches me when she has the chance. It is obviously nice when your family can watch you play but they do not affect the outcome of the match," said Murray.
Judy, though, seems to have had a beneficial effect on the women's game with excellent performance from all and with Elena Baltacha and Anne Keothavong in the second round and Heather Watson through to the third.
Murray was reluctant to ascribe that success to his mother. "I think in terms of the results in the Fed Cup and what the girls have done here, a lot of that is down to the coaches they have and the work done beforehand," he said, citing the work of Nigel Sears, once the head of women's tennis at the LTA and father of his girlfriend, Kim.
But he added: "I think it is nice for the women to have a female coach around. You do not see that very often. I think they probably understand the emotions the girls have better than guys do and the way they think."
Asked what his mother brought to players as a coach, Murray said: "My mum has always been about having fun and trying to make it enjoyable. If that has rubbed off on the girls and made them play better, that is a good thing."
Murray-Karlovic will be anything but fun on Centre Court. But Murray will take pleasure if he manages to cut a giant down to size.