The company also said currency controls in Venezuela made it impossible for airlines to convert their earnings into dollars and send the money abroad.
Venezuela's economy has been hit hard by a sharp drop in the price of oil - the country's main source of income.
Venezuela has high inflation and severe shortages of basic goods.
In a statement, Lufthansa said that it "will be forced to suspend our service between Caracas and Frankfurt as of 18 June".
It noted that the demand for international flights to Venezuela had dropped in 2015 and in the first quarter of the current year.
However, it said it hoped to restore services in the near future.
Strict currency controls were first imposed in Venezuela in 2003 by late President Hugo Chavez.
The restrictions were further tightened two years ago, forcing several airlines to reduce their operations in the country as they struggled to repatriate billions of dollars in revenue held in the local currency - the bolivar.
Some airlines are now requiring passengers to pay their fares in dollars.
Venezuela's government has defended its policies, saying it must prioritise.
Caracas says it is using its foreign reserves - which are now scarce - to pay for essential items such as medicines and industrial machinery.
The German airline, Lufthansa, has announced that it will suspend flights to Venezuela from 18 June due to economic difficulties in the country.