The 53-year-old was admitted yesterday morning after falling ill.
Reports last night said it is understood the manager was conscious and sitting upright in hospital, and was able to talk to medical staff and family.
Under Levein’s watch, Hearts have enjoyed a strong start to the season and currently top the Premiership table having won their opening three games.
The veteran boss was at Rugby Park on Saturday guiding his side to a 1-0 win over Kilmarnock thanks to an 81st minute strike. Levein gave post-match interviews and there was no suggestion he was unwell at the game.
The Capital club is not revealing the nature of Levein’s sudden illness but issued a brief statement on their website to confirm he was doing well but remained in treatment.
“Heart of Midlothian Football Club can confirm that manager Craig Levein as taken to hospital this morning,” said the statement.
“Having received medical treatment, Craig is now recovering well in hospital.
“No further comment will be made at this time and the club asks that Craig and his family’s privacy be respected, as we all wish him a speedy recovery.”
No timescale has been given for Levein’s return to work.
His assistant Austin MacPhee is preparing Hearts for their weekend match with St Mirren at Tynecastle Park.
Levein is in his second spell as Hearts boss.
The 53-year-old first took over as the Tynecastle outfit’s boss in 2000.
Spells at Leicester, Raith Rovers and Dundee United followed before Levein took over as Scotland boss in 2009.
He was relieved of his duties in charge of the national team in 2012.
After a spell out of the game, Levein returned to the Jam Tarts in the role of director of football in 2014 but signed a three-year contract as manager in August 2017 following the departure of ill-fated head coach Ian Cathro.
Naturally, Hearts fans took to social media in their droves to offer the man they regard a club legend a speedy recovery.
Hearts supporter @dig_our_scene tweeted: “Shocked to hear about Craig Levein taking ill today. Good news that he is doing well in hospital. Looking forward to seeing him back in the dug out when he has recovered.”
Bitter rivalries were set aside with hundreds of Hibs supporters also sending their best wishes. @jmendelsohn77 wrote: “Wishing all the best to Craig Levein for a swift recovery. Love from, a notional @HibernianFC fan.”
Cowdenbeath, Levein’s only playing club other than Hearts where he started out in 1981, said: “Cowdenbeath FC would like to pass on the best wishes of everyone at Central Park to ex-Cowden player and manager Craig Levein and his family.”
Dundee’s official twitter account said: “We would like to pass on our best wishes to @JamTarts Manager Craig Levein. We wish him a very speedy recovery.”