Mallzee said the cash would allow it to “scale its global offering”.
The company was founded in 2013 by 27-year-old Edinburgh-based entrepreneur Cally Russell.
Mr Russell pressed ahead with developing the app after turning down an offer of investment on the BBC’s Dragons’ Den programme.
Mallzee is a personalised shopping app, which allows users access to more than 100 fashion stores at one go. It also lets shoppers build their own “style feeds”.
Mr Russell said: “This round of investment is going to allow us to become the leading fashion shopping app in the world and the mix of investors is going to be vital to allowing us to achieve this. With Royal Mail Group we have a partner that plays a vital part in the online shopping environment and one which is well positioned to enable us to access new retailers.”
Earlier this year, Mallzee secured an exclusive promotional link-up with tech giant Samsung.