Von der Leyen set out the figures in a seven-page internal letter to the members of the CDU's youth wing.
"At stake is nothing less than the legitimacy of the pension system for the younger generation," said von der Leyen in the letter, details of which were published by the Bild am Sonntag newspaper on Sunday.
According to the numbers calculated by her office, workers who today work full-time for 35 years and earn less than €2,500 before tax per month would receive less than today's basic pension of €688.
This is because of a fall in basic pensions from 51 percent to 43 percent of the average German wage, she wrote.
The minister said those who make no other provisions than basic pension contributions would have to "make their way to the welfare office" on retirement.
Von der Leyen also claimed that those who work full-time for 40 years would need to earn at least the equivalent of €2,200 per month to be sure of a pension higher than the basic amount.
She added that 40 percent of lower-income earners who pay into the mandatory system did not pay into a private scheme.
"Many do not realise that they are also among those threatened by poverty in old age and that there is a compelling need for them to pay into an additional pension if they are to escape the poverty trap," she said.
The minister calls for a change to her preferred model for the pension system, which she said would provide for a pension supplements to a level of €850. The idea has met with resistance not only from junior coalition partners the pro-business Free Democratic Party, but also from within von der Leyen's own conservative Christian Democrats.
"It would cost millions," FDP leader Philipp Rösler told Welt am Sonntag. "We do not have the money for that in the pension fund."
The coalition is due to decide on reforms to the pension system this autumn.