  The bipolar nebula Menzel 3 (Mz 3) was observed as part of the
\textit{Herschel} Planetary Nebula Survey (\textit{HerPlaNS}), which used the
PACS and SPIRE instruments aboard the \textit{Herschel Space Observatory} to
study a sample of planetary nebulae (PNe). In this paper, one of the series
describing \textit{HerPlaNS} results, we report the detection of H I
recombination lines (HRLs) in the spectrum of Mz 3. Inspection of the spectrum
reveals the presence of 12 HRLs in the 55 to 680 $\mu$m range covered by the
PACS and SPIRE instruments (H11$\alpha$ to H21$\alpha$ and H14$\beta$). The
presence of HRLs in this range is unusual for PNe and has not been reported in
Mz 3 before. Our analysis indicates that the HRLs we observed are enhanced by
laser effect occurring in the core of Mz 3. Our arguments for this are: (i) the
available Mz 3 optical to submillimetre HRL $\alpha$ line intensity ratios are
not well reproduced by the spontaneous emission of optically thin ionized gas,
as would be typical for nebular gas in PNe; (ii) the compact core of Mz 3 is
responsible for a large fraction of the Herschel HRLs emission; (iii) the line
intensity ratios for Mz 3 are very similar to those in the core emission of the
well known star MWC 349A, where laser effect is responsible for the enhancement
of HRLs in the Herschel wavelength range; (iv) the physical characteristics
relevant to cause laser effect in the core of MWC 349A are very similar to
those in the core of Mz 3.
