Novak Djokovic is missing a Grand Slam tournament for the second time this season because he is not vaccinated against COVID-19.
Alcaraz had a chance to break into World No. 4 but had to settle for No. 5 after losing in the Hamburg European Open final against Lorenzo Musetti.
The slip is due to the men's tour governing body's controversial decision not to award ranking points for the Grand Slam event.
The last time the Swiss maestro was this far down in the ranking was in February 2000, when he was 18 years in age. He was ranked number 67 back then.
The 14th French Open title and his 22nd Grand Slam crown helped Rafael Nadal move up a place from fifth to fourth in the latest ATP Rankings released.
Novak Djokovic extended his record at the top of the ATP rankings to 370 weeks on Monday while Rafael Nadal drops down a place to number five.
Spain's Rafael Nadal retained the top spot in the men's ATP rankings in front of his old rival Roger Federer as Wimbledon kicks off on Monday.
Queen's Club champion Marin Cilic moved up a spot to fifth after his win over Novak Djokovic, who moves back into the top 20.
Coric, the Croatian outsider ranked 34th, also ended Federer's 20-match win streak on grass which stretched to June, 2017.
Rafael Nadal is 100 points ahead of Roger Federer going into the grasscourt season where the Swiss will be looking to close the gap.
Rafael Nadal's surprise quarter-final exit at the Madrid Masters has seen the Spaniard replaced as world number one by Roger Federer.
Rafael Nadal remained atop the ATP rankings released Monday after breezing to his 11th Barcelona title over the weekend.
The 21-year-old displaced Marin Cilic after his progress to the Monte Carlo Masters semi-finals won on Sunday for the 11th time by Nadal.
Nadal dethroned Switzerland's Roger Federer, who fell to the second place after he lost 3-6, 6-3, 7-6 (4) to Australia's Thanasi Kokkinakis at Miami Open's round of 64.
With 10,370 points, Murray continued to lead the rankings of the last week, a position he has managed to maintain since November 7.
Britain's Murray remains top ahead of Serb Novak Djokovic and Swiss Stan Wawrinka, who were all early casualties in Monte Carlo.