Sir Lindsay called a halt to proceedings after the leak started above the press gallery in the upper tier of the chamber.
MPs were distracted as they discussed a serious tax matter affecting their constituents when water began pouring from the ceiling.
Conservative former minister Justine Greening stared nervously upwards at the leak, which began as she spoke.
Proceedings carried on for a few minutes, but the noise of water pouring into the press gallery soon became overwhelming.
Labour MP Justin Madders (Ellesmere Port and Neston) added: "I hope I can complete my speech before rain stops play.
"I think there is probably some kind of symbol about how many people view how broken our Parliament is."
Senior Tory Sir Bill Cash (Stone) added: "I just wondered what is going on? Is it hot air escaping here?"
Sir Lindsay replied: "Somebody might say there is a leak in Parliament at the moment, we'll take it from there."
Mr Madders added: "I'm sure many Cabinet meetings have similar difficulties."
The Commons sitting was eventually adjourned at 3.13pm - more than two hours earlier than scheduled.
Speaking outside the chamber, Conservative former minister Sir Peter Bottomley told the Press Association: "We will obviously need a leak inquiry.
"It demonstrates we must have restoration and renewal. But we are very grateful to the maintenance staff who keep this place going."
A multi-billion-pound restoration of Parliament has faced delays despite repeated warnings about the Unesco World Heritage Site's state of disrepair.
Conservative MP Ross Thomson tweeted: "Not the first time there has been a leak in Parliament I'm sure."
A House of Commons spokesman said: "The leak was urgently dealt with and has now been isolated.
"The House of Commons maintenance team is currently assessing the damage.
"We would like to clarify this was not a sewage leak."