Nugent, who was arrested moments after he allegedly drove his Toyota LandCruiser into the MP, appeared in court to face three charges: dangerous driving causing serious injury, intentionally causing serious injury, and causing harm to a Commonwealth public official.
Police said more charges might be laid, including attempted murder.
His lawyer said his client had "mental health concerns" but did not give any further detail.
Victoria Police has said its investigation, with support from the Australian Federal Police, remains ongoing and a motive is yet to be established.
Investigators are looking into whether drug use or medication played a part in the incident.
Nugent's family has said they were long-time friends with Haines.
Shortly after the alleged attack, Australian Prime Minister Anthony Albanese told ABC television that there had been a "rise in temperature" and "too much shouting, not enough discourse" in Australia.
Haines, known for stances such as supporting stronger climate action, entered parliament in 2019 after working as a nurse and midwife.