No. Mahatma Gandhi and Indira Gandhi were not related. Indira Gandhi's got her surname from her husband Feroze Gandhi. In fact, it is not actually "Gandhi", it is "Gandhey" which is one of the surnames of Parsis, which later on became "Gandhi".
Indira Gandhi was originaly Indira Nehru, daughter of Jawaharlal Nehru. She was titeled Gandhi when she was married to Feroze Gandhi, a zoroastrianisth from Bombay on 26th March, 1942. They had two sons Rajeev and Sanjay Gandhi.