Wine is saying that Mono package is not installed, but I installed it with Terminal by:
sudo apt-get install mono-complete
What should I do?
Do the following to install wine-mono:
wine64 uninstaller to launch "Add/Remove Programs":

Installing .NET instead should work as well. For example by the following commands in a terminal:
sudo apt-get install winetricks
winetricks dotnet45
Other answers were not working for me on 18.04 LTS with winehq-stable package.
The workaround I found was to recreate wine32 and wine64 prefixes and install wine-mono on that with the automatic prompt.
# Create dir for 32 bit prefix
mkdir ~/.wine32
# destroy default configuration (64 bit prefix)
rm -rf ~/.wine
# Initial setup (create prefixes)
WINEPREFIX="$HOME/.wine32" WINEARCH=win32 wine wineboot
WINEPREFIX="$HOME/.wine" WINEARCH=win64 wine64 wineboot
# To install dotnet35 on 32-bit prefix
WINEPREFIX="$HOME/.wine32" WINEARCH=win32 winetricks dotnet35
@PSN's answer worked for me, however I was in the situation of needing to do this from a script on a remote CI machine without a user interface available.
I suggest the following solution, which worked for me:
wine msiexec /i wine-mono-7.4.0-x86.msi.It's also possible to verify on the command line that installing Mono worked:
$ wine uninstaller --list
{47A1FA26-B71E-5325-8161-20CF885181FF}|||Wine Mono Runtime
{7426CCE2-5341-534D-BAB0-1DAEDCCE76CE}|||Wine Mono Windows Support
Side note: it's also possible to run the installer using wine start wine-mono-7.4.0-x86.msi. While there's no graphical installer coming up for the Mono MSI on a local machine, it does not work like this on a headless machine. Fortunately wine msiexec /i wine-mono-7.4.0-x86.msi seems to work without a display though.
To install the right Wine Mono, you can find supported version in appwiz.cpl file as per suggestion from here.
$ locate appwiz.cpl
/usr/lib/x86_64-linux-gnu/wine-development/appwiz.cpl
$ grep -aho 'w.i.n.e.-.m.o.n.o.-.[^-]*-.[^.]*..m.s.i.' /usr/lib/i386-linux-gnu/wine*/appwiz.cpl | head -n1
wine-mono-5.1.1-x86.msi
Then download it from https://dl.winehq.org/wine/wine-mono/.
$ wget https://dl.winehq.org/wine/wine-mono/5.1.1/wine-mono-5.1.1-x86.msi
And run the installer:
$ wine start wine-mono-5.1.1-x86.msi
Or run wine uninstaller and select the installer file.
Check also the following helper script at install-wine-addon.sh.