One Twitter user said 'not really something to make jokes about', while another said 'poor that, pretty insensitive'.
Another social media user condemned Lineker by tweeting: 'First time I've ever disagreed with your humour. Not the time or place.'
The 55-year-old is a frequent Twitter user having posted over 18,300 tweets since joining the social media network in January 2012.
Lineker has previously been warned about his conduct on Twitter by the BBC.
The former Tottenham and Barcelona forward tweeted 'Bloody hell' and 'F***ing hell' after Leicester came from behind to beat Manchester United 5-3 in September 2014.
A BBC spokesperson told the Telegraph: 'Gary's is a personal Twitter account but we regularly remind him of his responsibilities around football based tweets.'
Lineker replied to newspaper reports about his tweet in September 2014 by tweeting: 'Dear papers, if I can't swear when Leicester come from 2 goals down to beat Man Utd 5-3 then I never can. Thanks though for your concern.'
His recent tweet came just three days after Brussels, Belgium's capital city, was attacked by terrorists.
Lineker tweeted on the day of the attacks: 'Human beings destroying human beings all over the world. Incomprehensible and unstoppable!'
The attacks claimed 31 lives, including Brit David Dixon, and injured an estimated 270 people.
Hodgson, who was speaking ahead of England's upcoming friendlies against Germany and Holland, will be hoping his side's next two games pass without incident.
England face Germany in Berlin on Saturday before hosting Holland at Wembley Stadium on Tuesday.