3 weeks or more. Most ssris start to show effectiveness against depression about 2 weeks after starting them. Prozac (fluoxetine) is about 1 week slower due to its long half-life (it takes longer to reach a steady blood level). So a good estimate is about 3 weeks. But everybody's different; some people feel better faster, others need to wait longer. Also, improvement is gradual, it doesn't become "effective" all at once.