A large emergency presence was called to the scene of the incident, which occurred near the A199, Wallyford, around 1.30pm.
Pictures from the scene show a lorry on its side in the middle of the train tracks near the village station.
The lorry driver was taken to hospital by ambulance, but his medical condition is not yet known.
The Scottish Ambulance Service has been contacted for comment.
A Police Scotland statement said: “Officers were called to reports of a lorry on the railway tracks near the A199, Wallyford, Musselburgh around 1.30pm on Thursday, 23 June, 2022.
“The male lorry driver has been taken to hospital by ambulance.
“Emergency services are currently at the scene and the following roads are closed:
“A199 closed between the Dolphinstone junction and Strawberry Corner roundabout.
ScotRail trains, which had been all but cancelled due to strike action, reported delays due to the incident, with the transport company taking to social media to confirm: “We have had a report of a lorry on the track between Wallyford and Prestonpans.
“Due to the lorry being close to the overhead wires the power has been turned off for safety reasons, the power is affecting services into and out of Edinburgh.”
National Rail posted a picture of the incident, adding: “We're working with the emergency services to find the best way to recover the HGV.
"Once that's done, we'll then need to check for damage to the track and overhead line kit.”
Rail services have been drastically reduced across the country following a nationwide walkout amid bitter pay disputes between RMT union members and Network Rail.
Asked during First Minister’s Questions on Thursday whether she believes the UK Government’s reported proposals to replace strikers with agency staff is “inflaming” the issue, Ms Sturgeon said it is workers who are paying the price.
Downing Street has announced plans to change the law to enable businesses to supply skilled agency workers to plug staffing gaps during industrial action.
However the plans have been branded “shameful” by union bosses.
Ms Sturgeon said she understands the dangers of the dispute “escalating” if a resolution is not reached between rail employers and unions.
She added: “[Workers] are paying the price for Tory anti-trade union rhetoric, in fact, anti-trade unionism which I completely deprecate.
“We should respect workers across the economy. We should respect public sector workers and we should seek to negotiate fair resolution to disputes, particularly at a time of inflation – inflation being exacerbated in the UK by the folly of Brexit.
“The rail strike that is crippling the UK right now is not the result of a pay dispute with ScotRail. It is a dispute with Network Rail and with English train operating companies, therefore it is entirely a reserved matter.
“And the other thing I remember from a few weeks ago in this chamber when there was a potential for a ScotRail dispute, Tory MSPs getting up and demanding intervention from this Government to resolve it.
“So let me repeat the call today for the UK Government to start doing their job to get round the table to bring a resolution to this and to drop the anti-trade unionism and have some respect for workers across the economy.”