Yes, suicide rates was that high!
Suicide in Nazi Germany by Christian Goeschel referenced in this essay says that
Goeschel’s study of suicide in Nazi Germany (2009) shows that the number of suicides varied greatly as the War progressed, as far as can be determined. Following the First World War the German suicide rate climbed steadily from just under 16 per 100,000 to 29 by the early 1930s
Wikilink about demographics in Germany (Kudos to Andrew Grimm) say that in the 1930s there were about 65M-69M people living in Germany.
Taking the extremes of 29 per 100,000, and 70M gives a number around 20K. What Hitler said does not seem farfetched thus.
The mass suicides during the loss of the war probably were even higher though.
The Mass suicides
Just over 7,000 suicides were reported in Berlin during the year 1945,
but it is thought that many suicides went unreported due to the chaos
of the post-war period.
Probably that year the number was EVEN higher.