Curtin was raised in County Limerick, near Kilmallock. The Curtin family have run a dairy farm between Banogue and Athlacca since the 1940s and Marie's parents, Sean and Eileen, took over the farm in 1975. She is one of seven children, with three brothers and three sisters. She began playing association football on the farm with her siblings and their friends from an early age. Curtin attended Ard Scoil Mhuire in Bruff. Between 2004 and 2008 Curtin attended Hofstra University on a four-year full soccer scholarship where she gained a BA in social sciences.
Association football
Lifford Ladies
Throughout her career Curtin played regularly for Ennis-based Lifford Ladies. In 2001 Curtin was named FAI Under-19 Women's International Player of the Year while playing for Lifford. She also made her senior debut for the Republic of Ireland while a Lifford player. Marie's sister, Anne Curtin, also played for Lifford Ladies and was a university international. The Curtin sisters helped Lifford Ladies reach the 2003 FAI Women's Cup final which they lost 2–0 to UCD. Marie Curtin subsequently guested for UCD in their 2003–04 UEFA Women's Cup campaign.
Curtin has played at a semi-professional level. Between 2005 and 2008, while attending Hofstra University, Curtin also played for Long Island Fury in the Women's Premier Soccer League. On May 20 2005, Curtin scored the first three goals in the team's history, scoring a first half hat-trick as Long Island defeated Northampton Laurels 5–0 as they made their WPSL debut. Curtin had a second spell as a semi-professional when she played for Fortuna Ålesund during the 2012 Norwegian First Division season.
Women's National League
Before the establishment of Women's National League, Curtin was playing junior football with Kilmallock United. In 2010 Curtin helped them reach the FAI Women's Junior Cup final which they lost 1–0 to Bohemians. The inaugural 2011–12 Women's National League season saw Curtin playing for Cork Women's F.C.. The 2014–15 season saw Curtin sign for Galway W.F.C.. By 2017 Curtin was playing for Aisling-Annacotty in the Limerick Women's & Schoolgirls' Soccer League. In 2018 she made a return to the WNL with Limerick.
Republic of Ireland
Curtin has represented the Republic of Ireland at under–16, under–18 and under–19 levels. Between 2000 and 2012 Curtin won 45 caps while representing the senior team. She made her debut for the senior team, aged just 16, in a behind closed doors friendly against Arsenal Ladies. She won her first full senior cap against Greece. Curtin represented the Republic of Ireland in qualifying campaigns for the 2005, 2009 and 2013 UEFA Women's Euros and the 2007 and 2011 FIFA Women's World Cups. Curtin also represented Ireland at the 2007 Summer Universiade.
In 2013 Curtin and her father, Sean, co-founded a dairy foods company, Temple Dairy Ltd. The company's main product is a healthy chocolate milk drink. Curtin is the company's managing director. In April 2017 Curtin promoted her product on an edition of Dragons' Den.