"Therefore, we reject the use of full-body coverings in public," the party said in its 18-page resolution on Thursday.
The resolution will be debated by CDU delegates at a crucial congress starting December 13.
Wearing veils is not illegal in Germany presently but in 2003 the federal constitutional court ruled that state governments could impose restrictions on school teachers.
As a result, half of Germany's 16 state governments banned teachers from wearing full body veils and headscarves. In March this year, however, the constitutional court struck down the ban as unconstitutional.
The new CDU demand comes at a time when the country is facing an influx of refugees, the highest in Europe, primarily from conflict-ridden Muslim countries in the Middle East and Afghanistan.
The upcoming CDU congress is likely to test Merkel's authority amid calls by some members for a cap on the number of refugees entering Germany.
The CDU in its main resolution resisted calls by some members for an "Obergrenze", or cap on the number of refugees entering Germany where roughly one million asylum seekers, many from Syria, Iraq and Afghanistan, are expected to arrive this year.
In order to tone down the calls for a refugee cap, the CDU has proposed a tougher ban on veils.
France has already enforced a complete ban on the burqa. The French government's prohibition was upheld by the European Court of Human Rights in July when a citizen moved the court against the ban.
Wearing the burqa in public in France now carries a fine of up to $164.
In the past, other European countries like Belgium, the Netherlands, Italy and Spain have also called for a ban especially on the full face-covering "niqab" and some have managed to implement it in parts.
In 2011, the Belgian government banned the Islamic full-face veil and any clothing that obscured a person's identity in a public place.
In 2007, the Netherlands prohibited the full veil in schools and on public transport. Veils have also been banned in several towns in Italy such as Novara.