Monday's announcement came after last week's election, in which Dias da Costa ran against President Umaro Sissoco. Sissoco has since been forced from power in a coup the day before the election results were due to be announced.
Opposition leader Dias da Costa is also considered to be under threat after the coup.
"The decision by the Federal Government of Nigeria to offer asylum and protect Fernando Dias da Costa is part of Nigeria's responsibility for sovereignty and long-standing commitment to regional peace, stability and democratic governance," State Department spokesperson Alkasim Abdulkadir wrote in a statement.
The opposition party PAIGC in Guinea-Bissau states that the party's headquarters have been "illegally occupied by heavily armed militia groups" in Bissau after the coup.
Opposition leader Dias da Costa has claimed that he won the presidential election against then-incumbent President Sissoco.
