The woman, who is identified in court papers by the initials B.A.N., said Foster and members of his family pressured her from October to December to abort the pregnancy after she told him about it, the Houston Chronicle reported Monday.
USA Today reported the woman has been identified as Brittany Norwood, 20, a University of Houston senior. The newspaper said the baby is due in June.
Foster was married in 2011 and has two children with his wife, Romina.
The former all-pro rusher carried on the affair over the summer and fall of 2013, the suit alleges.
The plaintiff is seeking undisclosed financial compensation for loss of past and future wages and exemplary damages for "conduct evidencing actual malice."
Foster's lawyers filed a general denial of the suit but declined to comment.