The 12.64-km section will significantly reduce travel time between Noida and south Delhi.
It is part of the Botanical Garden (Noida)-Janakpuri West (Delhi) corridor.
Modi will also address a public meeting in Noida.
This is the third metro line in the country to be inaugurated by the prime minister this year.
Modi had earlier dedicated Kochi Metro to the nation in June and Hyderabad Metro in November.
Also Read
Recently, a metro train of the Magenta Line crashed into a wall at Kalindi Kunj depot after it rolled back on a ramp while being taken for washing.
There were no casualties, according to the Delhi Metro Rail Corporation (DMRC) which had blamed the incident on "human error and negligence" during maintenance.
DMRC had also asserted that it would have no bearing on the launch.
The official statement further said that the prime minister has often used the metro to travel for engagements in the National Capital Region.
In January 2016, the prime minister and the then French President Francois Hollande travelled in metro from Delhi to Gurgaon to jointly lay the foundation stone of the headquarters of the International Solar Alliance.
More recently, in April 2017, Modi and his Australian counterpart Malcolm Turnbull travelled by metro to the Akshardham Temple.
"In keeping with the objective of enhancing connectivity through mass rapid transit systems, the union government has launched nine metro projects covering a stretch of nearly 165 kilometres over the past three-and-a-half years.
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