Interior Minister Horst Seehofer waved Ms Merkel’s hand away at a meeting with migrant groups in Berlin.
The meeting follows the news that Germany has updated the number of people confirmed to be infected with the Covid-19 virus to 150.
President of the Robert Koch Institute, Lothar Wieler, said the situation in Germany had developed “very dynamically”.
In the UK, the number of total cases of Covid-19 has reached 40, according to chief medical officer Professor Chris Whitty.
No advice around shaking hands has been issued by Public Health England.