The consumer electronics chain said Chief Financial Officer Jim Gooch will replace Day.
Daniel Feehan, the board's current presiding director, will become non-executive chairman of the board upon Day's retirement, the company said in a statement.
For the fourth quarter, RadioShack expects to earn 50-54 cents a share, while analysts on average expect a profit of 66 cents a share, according to Thomson Reuters I/B/E/S.
Preliminary total net sales for fourth quarter increased about 4 percent to $1.37 billion, while same-store sales rose about 1 percent.
The Fort Worth, Texas-based company's shares were down 11 percent at $15.66 in Monday morning trade on the New York Stock Exchange.
(Reporting by Viraj Nair in Bangalore; Editing by Anne Pallivathuckal)