To answer the general question: It depends on several factors.
The role you are applying to. I found that for junior technical positions, not necessarily limited to software engineering, introverted personality traits are much more widely accepted, even preferred in some cases. There seems to be a somewhat widespread (and at least partially misguided) understanding that being introverted is directly correlated to technical proficiency or the willingness to work long hours. The more senior you become with regards to your position, especially if you are moving towards a leading position in a team, the more willingness to effectively communicate with business partners, customers or superiors is expected. I'm not saying that being an introvert means one is unable to do that.
The person / department conducting the interview. Especially in bigger companies, with a dedicated HR-department doing the first round of interviews, being an introvert can influence your interview in a negative way. From my limited experience in a position where I was only able to look at candidates that have been pre-selected by HR, the process was focused on applicants hitting certain keywords (be it certain phrases that were used or even very specific technologies that were talked about), not on applicants being a good fit for the position. If the interview is done by the (fictional) team-lead of the (fictional) team you are (fictionally) applying to, chances are that he / she is able to correctly assess the situation.
Your definition of introverted. If you are someone who prefers solitude, but has no trouble socializing or functioning socially when business requires it, that won't ever really be a problem. If you are unable to deal with an interview situation, which can admittedly be quite stressful, and resort to short answers and show an inability to follow expected social norms, that might negatively influence your interview outcome.
To answer your more specific question: Judging from the way you are describing it, you're going to be perfectly fine.
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To answer the general question: It depends on several factors.
The role you are applying to. I found that for junior technical positions, not necessarily limited to software engineering, introverted personality traits are much more widely accepted, even preferred in some cases. There seems to be a somewhat widespread (and at least partially misguided) understanding that being introverted is directly correlated to technical proficiency or the willingness to work long hours. The more senior you become with regards to your position, especially if you are moving towards a leading position in a team, the more willingness to effectively communicate with business partners, customers or superiors is expected. I'm not saying that being an introvert means one is unable to do that.
The person / department conducting the interview. Especially in bigger companies, with a dedicated HR-department doing the first round of interviews, being an introvert can influence your interview in a negative way. From my limited experience in a position where I was only able to look at candidates that have been pre-selected by HR, the process was focused on applicants hitting certain keywords (be it certain phrases that were used or even very specific technologies that were talked about), not on applicants being a good fit for the position. If the interview is done by the (fictional) team-lead of the (fictional) team you are (fictionally) applying to, chances are that he / she is able to correctly assess the situation.
Your definition of introverted. If you are someone who prefers solitude, but has no trouble socializing or functioning socially when business requires it, that won't ever really be a problem. If you are unable to deal with an interview situation, which can admittedly be quite stressful, and resort to short answers and show an inability to follow expected social norms, that might negatively influence your interview outcome.
To answer your more specific question: Judging from the way you are describing it, you're going to be perfectly fine.