Spanish-born Garijo, 60, currently serves as the group's deputy chief executive officer and head of its healthcare unit.
She will replace Stefan Oschmann whose term ends next April after five years at the helm of the Darmstadt-based group.
“She knows our company extremely well and has done excellent work in transforming our healthcare business sector,” Johannes Baillou, chairman of Merck's board of partners, said in a statement.
Garijo will make history as the first solo female leader of a firm listed on Frankfurt's prestigious DAX 30 index.
German software group SAP made the first cracks in the glass ceiling last year when it appointed Jennifer Morgan as co-CEO alongside a male executive.
She stepped down in April after just six months however, as SAP decided to switch back to a sole CEO to steer it through the coronavirus upheaval.
Although Germany has been run by a woman chancellor for 15 years, female top executives remain a rare sight in Europe's top economy.
The German government introduced legislation in 2015 requiring women to make up 30 percent of supervisory board seats in large companies, and Chancellor Angela Merkel has voiced support for plans to introduce similar rules for executive boards.
Germany's gender pay gap is also one of the largest in Europe, with women earning about 21 percent less than men on average.
Garijo, who previously worked at Sanofi, joined Merck's healthcare unit in 2011.
She has been credited with overhauling the department's research and development and refocussing attention on fewer drugs with better prospects, boosting sales and profits, according to the Handelsblatt financial daily.