No, Klara was not Jewish.
The only question concerning Hitler's possible Jewishness revolves around his father Alois, who was the illegitimate son of a woman called Maria Anna Schicklgruber. She had once worked as a maid for a Jew called Leopold Frankenberger and it has been suggested that he was the father of Hitler's father Alois. However, most historians disagree with this and say that Johann Heidler, a miller, was Alois' father. This Johann Heidler eventually married Maria and was legally declared the father of Alois.
It was Alois, Hitler's father, who later changed his name from Schicklgruber to Heidler (although this was written as Hitler due to spelling being not unified at that time).
Hitler's mother
Klara Polzl
She did not have a middle name, she was born as Klara Polzl.
Klara Polzl (better known as Klara Hitler) died in 1907, a particuarly painful death due to poisoning from her treatment of Breast Cancer
On 12 August 1860.
Alois and Klara Hitler
Alois and Klara Hitler.
Klara Hitler (Polzl)
Klara Pölzl (better known as Klara Hitler) was a maid early in her life. After she married Alois, she became a housewife.
Alois Hitler and Klara Polzl
Adolf Hitler's parents were: Alois Hitler and Klara Pölzl.
Hitler's Parent's are Alois and Klara Hitler