Ms Yaqoob, who was the party leader, said she had no alternative but to quit following a breakdown of trust and collaborative working.
Her decision follows a public row with Respect MP George Galloway about rape and the case against Wikileaks founder Julian Assange.
She did not comment directly on Mr Galloway, but said the last few weeks had been “extremely difficult” for the party and for her and that she had taken a decision to resign “with deep regret”.
Mr Galloway, the MP for Bradford West, hit the headlines in August by appearing to suggest that consent was not needed each time before sex. He criticised the legal case against Mr Assange, who is wanted in Sweden to answer allegations of sexual assault against two women.
At the time, Ms Yaqoob described Mr Galloway’s remarks as “deeply disappointing and wrong”.
In a prepared statement, Ms Yaqoob said: “It is with deep regret that I have decided to resign from Respect. The last few weeks have been extremely difficult for everyone in the party.
“I feel necessary relations of trust and collaborative working have unfortunately broken down. I have no wish to prolong those difficulties, and indeed hope that they may now be drawn to a close.
“I remain committed to the principles and values that led me to help found Respect. The policies we have fought for need to be voiced as loud as ever in opposition to a political establishment that remains out of touch with working people.
“I would like to thank everyone in the party for their support over the years; I wish everyone the very best for the future and in those common struggles for peace, justice and equality that I am sure we will all continue to be involved in.”
Respect National Secretary Chris Chilvers said: “While we are obviously very sorry that Salma has decided to leave Respect, we would like to thank her for the great contribution she has made to Respect over the last decade. We look forward to working with Salma in the future in pursuit of our shared values and objectives.
Ms Yaqoob, a former city councillor for Sparkbrook, became politically active following the 9-11 terrorist attacks. She reported being spat at in the street in Birmingham after the atrocities.
She stood for Respect in the 2010 General Election, contesting Hall Green, where she came a close second to Labour MP Roger Godsiff, reducing his majority to 3,799 votes.
She resigned as a city councillor last year, citing health reasons.
However, she played an important campaigning role in the Bradford West by-election, which saw Mr Galloway win by a landslide.
Ms Yaqoob’s name has been linked in the past with Labour in Birmingham. It’s believed party members tried to convince her to join, although there is no evidence that their approaches were ever taken seriously.