It is possible to silently install msysgit using the following flags when called from a dos prompt:

/SILENT /COMPONENTS="icons,ext\reg\shellhere,assoc,assoc_sh"

An example of this is

Git-1.9.4-preview20140611.exe /SILENT /COMPONENTS="icons,ext\reg\shellhere,assoc,assoc_sh"

You can find all of the possible flags to use by inspecting the install.iss file:

https://github.com/msysgit/msysgit/blob/master/share/WinGit/install.iss

You can also load install parameters from a file with /LOADINF="filename", and you can record parameters to a file using /SAVEINF="filename".

An example of a parameter file is:

[Setup]
Lang=default
Dir=C:\Program Files (x86)\Git
Group=Git
NoIcons=0
SetupType=default
Components=
Tasks=
PathOption=Cmd
SSHOption=OpenSSH
CRLFOption=CRLFAlways

More information on commandline parameters can be found at http://www.jrsoftware.org/ishelp/index.php?topic=setupcmdline