Merkel will first travel to the Berlin residence of German President Frank-Walter Steinmeier to be officially nominated before returning to the Bundestag to be sworn in as Chancellor later in the day.
Before two police officers brought him down, the man shouted "Please, Mrs. Merkel, help me".
Merkel's newest, and probably her last, team "is much like her - dependable, if a bit boring", says Politico. "Mrs. Merkel help, please".
Her likely final term may prove her most challenging yet as she takes charge of a fragile coalition with her personal standing diminished.
Lawmakers voted 364-315 on Wednesday to re-elect Merkel, who ran unopposed.
It is almost six months since the election.
While including new faces, Merkel's pick of cabinet members includes longtime allies from her Christian Democratic Union.
The coalition of Ms Merkel's conservative Christian Democratic Union, its Bavaria-only sister party, the Christian Social Union and the centre-left Social Democrats have 399 of the 709 seats in parliament.
Merkel enters her new term with a possible trade war looming. But after Ms Merkel's talks with two smaller parties failed in November, she turned to the SPD out of desperation and asked them to prolong the "grand coalition" that has governed Germany since 2013. Yet policies pledged by Merkel's new government are unlikely to defuse the conflict, with the current-account surplus probably rising to 8.1 percent of economic output this year, the third-highest since 1993, according to the DIW economic institute in Berlin.
"We have a lot of work ahead of us", Merkel said after the formal signing of the coalition deal with the SPD on Monday.
Merkel, 63, has long dismissed the notion that she should be regarded as the "leader of the free world" following the election of Trump, who is unpopular in Germany and elsewhere in Europe.
Responding to criticism within her ranks, the fourth Merkel cabinet is younger and nearly evenly split between men and women.
In what The Guardian describes as a nod "to the language and concerns of the far-right", Merkel vowed that her government would be a "grand coalition for the little people".
Aside from managing her coalition partners at home, Ms Merkel also faces a growing list of worldwide challenges, such as a potential Europe-US trade war, a fraught relationship with Russian Federation and France's calls for closer ties between European Union nations.