  Rydberg atoms have great potential in electric field measurement and have an
advantage with a large frequency bandwidth from the kHz to the THz scale.
However, the sensitivity for measuring a weak MHz electric field signal is
limited by the spectroscopic resolution, because the weak electric field
induces only a small perturbation of the population and energy level shift of
the Rydberg atoms. Here, we report highly sensitive measurement of a weak MHz
electric field using electromagnetically induced transparency with Rydberg
atoms in a thermal atomic system. Using the heterodyne method on a 30-MHz
electric field, we successfully measure the minimum electric field strength to
be \textcolor{black}{37.3 $\mathrm{\mu V/cm}$} with a sensitivity up to $-65$
dBm/Hz and a linear dynamic range over 65 dB. Additionally, we measure an
amplitude-modulated signal and demodulate the signal with a fidelity over 98\%.
This work extends the sensitivity of atomic sensors for measuring MHz electric
fields, which advances atomic electric field-sensing technology.
