The woman, who has not been named, can be seen shouting "bitch" at Merkel in a video on YouTube, tabloid Bild reported.
Police told AFP that an investigation has been opened into "anti-constitutional slander against constitutional organs" of state.
The probe is "targeted at the comments made loudly" by the woman who was protesting alongside far-right demonstrators and carrying a placard reading "traitor".
Asked about the insults levied at the German leader, Merkel's spokesman Steffen Seibert said the chancellor did not plan to press charges.
"There will be no tolerance of those who question the dignity of other people," the German leader said during her visit.
"The more people who make that clear... Through their work and also in conversations with acquaintances, friends and families, the stronger we will be and the better we will be able to address this task" of caring for refugees, she added.
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