The three plaintiffs said they survived a 2012 US drone strike that killed two of their relatives and that the fear of another attack had turned their family lives into "a constant nightmare from which we can't wake up".
However, the Cologne administrative court found that the German government is "under no obligation to prohibit the United States from using the Ramstein Air Base to conduct drone strikes in Yemen".
The court said it agreed that in principle Germany had a duty to protect people against danger to life and limb emanating from its territory.
But it also found that the government had some "leeway in its assessment, evaluation and actions" when it came to foreign policy matters, according to the ruling by presiding judge Hildegund Caspari-Wierzoch.
"In addition, the agreements on the deployment of friendly forces in Germany provide for only very limited influence by German authorities on the use of the properties by foreign troops," a court statement said.
The court also said the government had repeatedly and recently asked the US "to respect German and international law" in its Ramstein operations and that "the American government has promised to do so".
The plaintiffs, represented by the Berlin-based European Center for Constitutional and Human Rights (ECCHR), had argued that the air base relays signals from US-based operators to the aerial vehicles flying over Yemen.
The ECCHR's head Wolfgang Kaleck said the group "regrets" the ruling and was considering an appeal, arguing that "Germany is making itself complicit in the deaths of civilians as part of the US drone war".
"See nothing, hear nothing, say nothing -- with this strategy the government cannot and will not be able to meet its obligation to prevent human rights violations committed by the USA via German territory."
The complaint was filed, together with ECCHR and London-based rights group Reprieve, by Yemeni citizens Faisal bin Ali Jaber, Ahmed Saeed bin Ali Jaber and Khaled Mohmed Naser bin Ali Jaber, who did not attend the hearing.
Washington has for years launched drone strikes targeting suspected Al-Qaeda militants in Yemen, an impoverished country that in recent months has been torn by fierce fighting between its beleaguered Saudi-backed government and Iran-backed rebels.
Germany's Spiegel news weekly and other media have reported that Ramstein is used as a signal relay station that allows military personnel in the United States to remotely steer drones and launch attacks as far away as Afghanistan, Pakistan, Yemen or Somalia.