Joshi's demand was backed by the Congress whose general secretary in-charge of UP Digvijay Singh said the UP police could not be trusted in the matter.
Her house was vandalised and set on fire on July 15. "To avoid any controversy and ensure an unbiased inquiry into the incident, the government has decided to transfer the probe to the CB-CID," Cabinet Secretary Shashank Shekhar Singh told mediapersons in Lucknow.
Joshi, who is charged with making derogatory remarks against the Bahujan Samaj Party supremo, alleged that the arson was a "state-sponsored crime" and demanded a CBI inquiry saying she has no hope of getting justice from the Mayawati government.
Congress's UP unit said the CID probe was an "eye-wash."
Joshi, who is due to meet Congress president Sonia Gandhi, apologised for her remarks and claimed that she had been "a bit misunderstood."
She is currently on interim bail. "I am sorry for what I said. My issue was right and it is a debatable one, The UP government is insensitive. They do not care for the women," she said in New Delhi.
The Congress leader said the comments were "an emotional outburst of a woman activist."
At the same time, she said "I will not defend myself on that second sentence (with regard to Mayawati). I withdraw it."
"I was embarrassed for that seven-second line that I made during a seven-minute speech, but the intention was not to demean any individual forget about a caste," she said, adding charges against her were disproportionate and illegal.