He said Mr Lungu, who is standing for the governing Patriotic Front (PF), "enjoys good health".
The spokesman said concerns about Mr Lungu's health had been raised by opponents as a "campaign tactic".
Two Zambian presidents, Levy Mwanawasa and Michael Sata, have died in office in the past seven years.
Zambian voters will go to the polls on 20 January to elect a permanent successor to Mr Sata, who died in October last year.
'Malicious'
Calls for Mr Lungu - currently Zambia's justice and defence minister - to undergo medical tests were made by a former PF politician, Sylvia Masebo, who has switched allegiance to the opposition United Party for National Development (UPND).
Mr Lungu's spokesman, Emmanuel Mwamba, told the BBC's Focus on Africa programme that the candidate was "ready to take any medical test at any time".
He stressed that there was no legal requirement for presidential candidates to submit to such tests but said Mr Lungu, who is thought to be 58, welcomed the opportunity to demonstrate his good health.
Mr Mwamba said his concern was over the "malicious manner" in which the request was made.He said it was made in an effort to undermine Mr Lungu's campaign and "scare our voters".
Mr Lungu has been a divisive figure, even within his own party.
Interim President Guy Scott suspended him as PF secretary-general following Mr Sata's death but was forced to reinstate him a day later following an outcry in the party.
There was further division over the selection of a presidential candidate, with two factions of the party holding separate conferences and choosing their own candidates.
The dispute went to Zambia's high court where it was resolved in Mr Lungu's favour.
