Helen Morgan had told Miss Patel to "tear up your copy of Goebbels' manual" when the pair clashed on Twitter about migrants crossing the English Channel in small boats.
After removing the comments, Mrs Morgan said: "I apologise for this insensitive tweet which I have taken down.
"I am focused on standing up for the people of North Shropshire who are being taken for granted by Boris Johnson's Conservatives."
The row started after Miss Patel posted on Twitter about the removal of a group of migrants who had crossed the channel in a small boat.
Miss Patel wrote: "They had previously claimed asylum elsewhere and had no legal right to be in the UK.
"Removals continue to be frustrated by activist lawyers, but I will not let up until this route is unviable."
But Mrs Morgan replied: "I think we would all appreciate an explanation of the difference between a lawyer and an activist lawyer.
"In the meantime, please tear up your copy of Goebbels' manual; it is most unbecoming of one of The Great Offices of State."
The row comes days after Mrs Morgan issued a separate apology for comments made on Twitter last year which appeared to liken Channel migrants to Jews held at Auschwitz.
She had also compared the PM's attempts to prorogue Parliament as acting like "what Hitler did in 1933" and described it as a "shameless power grab".
Mrs Morgan's comments were criticised by Tory MP Andrew Percy, chairman of the all-party parliamentary group against anti-semitism.
"Comparisons to the Nazis are not only sick, they are inaccurate, offensive and diminish the memory of the six million Jewish and other victims of the Nazi murder machine," said Mr Percy.
"Such throwaway comparisons undermine Holocaust education efforts and risk enabling antisemitism.
"The Lib Dems must act to take strong and immediate action against this candidate's repeated use of these sick and disgusting comparisons."