Currently internet access in Ukraine is fairly good but it is expected to deteriorate as the conflict worsens.
Meanwhile businesses are trying to get their hands on the dishes, as back-up systems.
Ukraine's deputy prime minister Mykhailo Fedorov asked for Mr Musk's help, and tweeted a picture of the Starlink dishes arriving.
Plug in the dish - or terminal as it's officially called - and it will automatically connect itself to the nearest Starlink satellite in the sky, of which there are more than 2,000.
The satellite then communicates with the nearest ground station, or gateway, which supplies the internet.
These gateways are located around the world, but they can't be too far away from the place getting an internet connection. Fortunately for Ukraine, there is a gateway in neighbouring Poland.
The internet connection travels from the gateway to the satellite, and then to the terminal. Users simply plug their router into their terminal and the tech takes care of the rest.
One of the major issues with previous iterations of satellite internet is the delay, but Starlink's constellation of satellites is a relatively new technology - they operate in low-Earth orbit, so the delay is measured in milliseconds rather than seconds.
Usually this would come at a cost. In the UK, it will cost you £495 for the dish (including shipping), and then a subscription of £89 per month. There is no indication that Ukrainians will be charged for the service.
The terminals need a clear view of the sky in order to work, and there is an app to help users find a suitable spot to place them.
Ordinary considerations are overhanging trees and other obstructions - in Ukraine, users will have to consider safety and how they may appear to Russian forces.
Once set up, the speed they offer varies but one user who already had access to a terminal tweeted on Monday that he had reached speeds in excess of 200 Mbps (megabits per second) for a while.
Business people, such as Stepan Veselovskyi, chief executive of Lviv IT Cluster, are trying to get their hands on more terminals, but are finding it difficult.
"We are trying to buy receivers but I am not sure whether we will succeed."
Currently internet services in most Ukrainian cities are working well but it will be important for businesses to have a contingency plan if networks fail, said Mr Veselovskyi.
NetBlocks, which is monitoring internet speeds in Ukraine, told the BBC it has seen internet collapse in some areas, such as Sievierodonetsk, the acting administrative centre of Luhansk Oblas.
"Friends and family report no contact with loved ones in recent hours" it tweeted last night. Currently the firm says it is seeing internet speeds at around 80% of ordinary recorded levels.
But Alp Toker of NetBlocks cautioned against seeing Starlink as a substitute for phone networks and broadband: "Starlink can provide connectivity by creating a personal hotspot for people who are in the vicinity of the device. So this is very useful for journalists, for resistance groups or the elected government."
Mr Toker said the devices would be most useful in providing a way of journalists and politicians getting information to the wider world, if there is a blackout in Kyiv.
"Even if it's only from the select few who have been chosen to receive these devices, it's better than having a total absence of information."
Some have questioned the safety of using satellite internet during a conflict, suggesting that the dishes could be targeted by Russian forces.
In a widely shared twitter thread John Scott-Railton, a senior researcher at The Citizen Lab, said that Mr Musk's offer of assistance was "good to see" but warned users to be careful, noting: "Russia has decades of experience hitting people by targeting their satellite communications".
But Mr Toker said that while "there is some risk when it comes to individuals being detected through, say, drones flying overhead", the greater risk to ordinary citizens was more likely to come from having to explain why they were in possession of the device.
Starlink is not the only satellite internet company operating in the region. Commercial satellite internet company Viasat said that on 24 Feb, the day Russia invaded, it suffered "a cyber-event" affecting broadband services.
The company has not said who or what is behind it, but said it was experiencing a "partial network outage" affecting internet service for fixed broadband customers "in Ukraine and elsewhere on our European KA-SAT network".