For any rank 2 Drinfeld module rho defined over an algebraic function field, we consider its period matrix P(rho), which is analogous to the period matrix of an elliptic curve defined over a number field. Suppose that the characteristic of the finite field F(q) is odd and that rho does not have complex multiplication. We show that the transcendence degree of the field generated by the entries of P(rho) over F(q)(theta) is 4. As a consequence, we show also the algebraic independence of Drinfeld logarithms of algebraic functions which are linearly independent over F(q)(theta).
