We show that the vacuum expectation value of the inflaton at the Peccei-Quinn axion scale can generate the supersymmetric Higgs mass $μ$ term. This provides an inflationary simultaneous solution to the strong CP problem and the $μ$ problem of the Minimal Supersymmetric Standard Model, and gives a testable prediction for the $μ$ parameter: $μ^2 \approx (0.25-0.5)m_0^2$, where $m_0$ is the soft Higgs scalar mass. Our model involves a very small Yukawa coupling of order $10^{-10}$, which could originate from an extra-dimensional scenario or type I string theory.

Version to appear in Physics Letters B. 14 pages