They say the decision was taken after more bad weather was forecast.
Performances were suspended on Saturday during continued thunderstorms, forcing many of the 92,000 fans at the open-air event to shelter in cars and tents.
Organisers were forced to cancel it after local authorities revoked its licence early on Sunday morning.
They said on Facebook (in German) that they regretted the decision but accepted it was necessary because the safety of fans was of paramount importance.
Critics on Facebook have accused organisers of not cancelling the event quickly enough.
Fans at Rock am Ring - held at the airport in the town of Mendig, about 100km (62 miles) west of Frankfurt - were told to clear the festival grounds by noon on Sunday.
At least eight people were seriously injured by the lightning strike early on Saturday morning.
Central Europe has been hit by severe storms and rain over the past few weeks, leading to 11 deaths in Germany.
The Rock am Ring festival - one of the most popular of its kind in Germany - also suffered lightning strikes last year, when 33 people were taken to hospital.
The festival website has repeatedly warned fans of the possibility of strong rainfall and thunderstorms.
The organisers of Rock am Ring, now in its 31st year, initially said on Saturday that this year's event would continue. It was due to have finished on Sunday evening.
Red Hot Chili Peppers were among several bands, including Black Sabbath, Foals, Deftones and We Are Scientists, who were on the line-up.
Last weekend, 35 people were injured, three seriously, when lightning struck a football match in south-west Germany. A further 11 people were hurt by a lightning strike in a Paris park where a children's birthday party was taking place.

Pernod Ricard, which is based in France, is the second biggest distiller of Scotch after Diageo.
Its brands include Chivas, The Glenlivet and Ballentine's.
However, the distiller reported that Jameson's, the biggest-selling Irish whiskey, continued to be the star performer among its premium brands.
American sales of the Cork-distilled whiskey were up more than 10%.
In its update for investors, the drinks company reported total sales rose 3% in the first three months of 2017, and the detail gave some pointers to the market for whisky and other drinks around the world.
Pernod Ricard reported the Chinese market "remains challenging for Scotch", while there were more positive sales figures for Martell brandy.
Imported spirits have been held back in China by official disapproval of conspicuous business hospitality and gifts. Bar and restaurant sales were reported to remain in decline.
The company said Korean sales continue a "strong decline" across its brands.
It also reported on the disruptive effect in India of the government removing large amounts of the nation's paper money from circulation, and a new law that will forbid the sale of alcohol close to highways.
In Latin America, which has been a strong growth area for Scotch exports, Brazilian sales were weaker due to prolonged recession. But sales across the Pernod Ricard brands were strongly up in other countries, led by Colombia, Argentina, Uruguay and Cuba.
The UK market was described as resilient and "dynamic", because its products were being imported ahead of price increases in March, linked to the weakening of sterling. Among the stronger performers were Absolut vodka and Jameson's.
With its full year results for 2015-16, Pernod Ricard reported Jameson's global sales were up 12% by volume and 16% by value.
In Scotch whisky, Ballentine's rose 5% by volume over the year, while Chivas was down 5% and Glenlivet single malt by 2%.
Another French company with a stake in Scotch whisky, Remy-Martin, this week reported that its sales of "Progressive Hebridean" spirits, including Bruichladdich and The Botanist gin, rose by more than 10% in the year to March.
The third and final day of the sell-out Rock am Ring music festival in Germany has been cancelled after lightning hurt at least 80 fans, organisers say.
[NEXT_CONCEPT]
One of the biggest Scotch whisky distillers has seen faster growth in sales of its Irish whiskey brand, according to new figures.