Evans, 34, fell at the back of the court in the first game of the deciding third set, letting out a loud cry and immediately signalling he could not continue.
The world number 59 has endured a tough season and looked to be in tears as he sat on his chair.
Having not won on the main ATP Tour since March, Evans played superbly to win the first set 6-4, before Nakashima levelled by taking the second 6-3.
“I’m heartbroken at the minute. It’s tough,” said Evans, who will have a scan in the next 48 hours to determine the extent of the injury.
“If I miss the Olympics or Wimbledon, it would be a tough one to swallow, no doubt.”
Evans was the latest player to fall victim to the slippery surface, with American Frances Tiafoe and Australia’s Thanasi Kokkinakis pulling out of matches because of injuries caused by the same court.
Queen’s officials said the “exceptionally cooler and wetter weather” in the UK over recent months has been a key factor.
“Grass courts are a living surface and will always react to weather conditions in the lead up to the event, usually having a tendency to play more slippery at the start of the tournament,” a tournament spokesperson said.
“The outstanding grounds team have done their very best to adapt to this, applying the same rigorous preparation as they always do.”
On the court next door, 29-year-old Harris continued his late-blooming ascent with a notable win over Etcheverry.
Harris, who only earned his first win on the ATP Tour last year, recorded a 6-4 3-6 6-3 victory in his first-round match.
As a result, he will climb to a career-high ranking inside the top 150 next week.
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